Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 11.3 Answer Key Generating Equivalent Expressions.

## Texas Go Math Grade 6 Lesson 11.3 Answer Key Generating Equivalent Expressions

**Essential Question**

How can you identify and write equivalent expressions?

**Texas Go Math Grade 6 Lesson 11.3 Explore Activity Answer Key**

**Explore Activity 1**

**Identifying Equivalent Expressions**

One way to test whether two expressions might be equivalent is to evaluate them for the same value of the variable.

Match the expressions in List A with their equivalent expressions in List B.

A. Evaluate each of the expressions in the lists for x = 3.

B. Which pair(s) of expressions have the same value for x = 3?

C. How could you further test whether the expressions in each pair are equivalent?

D. Do you think the expressions in each pair are equivalent? Why or why not?

**Reflect**

Question 1.

**Error Analysis** Lisa evaluated the expressions 2x and x^{2} for x = 2 and found that both expressions were equal to 4. Lisa concluded that 2x and x2 are equivalent expressions. How could you show Lisa that she is incorrect?

Answer:

According to Lisas conclusion x^{2} = 2x. If this was correct then this equation would have held true for all, values of x, but here this is not the case, as for x = 3, then 3^{2} = 9 and 2(3) = 6 and 9 ≠ 6

**Explore Activity 2**

**Modeling Equivalent Expressions**

You can also use models to determine if two expressions are equivalent. Algebra tiles are one way to model expressions.

Determine if the expression 3(x + 2) is equivalent to 3x + 6.

A. Model each expression using algebra tiles.

B. The model for 3(x + 2) has ___ x tiles and ___ 1 tiles.

The model for 3x + 6 has ___ x tiles and ___ 1 tiles.

C. Is the expression 3(x + 2) equivalent to 3x + 6? Explain.

**Reflect**

Question 2.

Use algebra tiles to determine if 2(x – 3) is equivalent to 2x – 3. Explain your answer.

Answer:

Algebra tiles for the given expressions.

The parenthesis makes a difference in the given expressions. Parenthesis indicates grouping or multiplication which makes the expressions not equivalent

2 (x – 3) = 2x – 6 which is different from 2x – 3.

The expressions are not equivalent because the value of both expressions will not be similar.

**Your Turn**

For each expression, use a property to write an equivalent expression. Tell which property you used.

Question 3.

(ab)c = ____

Answer:

The operation in the expression is multiplication

You can use the Associative Property of Multiplication to write an equivalent expression:(ab)c = a(bc) (Final solution)

a(bc)

Question 4.

3y + 4y = _____

Answer:

Given expression:

3y + 4y = 4y + 3y

According to Commutative Property of Addition

3y + 4y = 4y + 3y. According to Commutative Property of Addition.

**Your Turn**

**Use the properties of operations to determine if the expressions are equivalent.**

Question 5.

6x – 8; 2(3x – 5)

Answer:

Given expression:

2(3x – 5)

Apply dstributive property to expand the parentheses

= 2(3x) + 2(-5)

Expand:

= 6x – 10x ≠ 6x – 8

6x – 10x ≠ 6x – 8

Question 6.

2 – 2 + 5x; 5x

Answer:

Determine if the expressions are equivalent

0 + 5x = 5x identity property of addition

5x = 5x

The expressions are equivalent because of identity property of addition.

Question 7.

Jamal bought 2 packs of stickers and 8 individual stickers. Use x to represent the number of stickers in a pack of stickers and write an expression to represent the number of stickers Jamal bought. Is the expression equivalent to 2(4 + x)? Check your answer with algebra tile models.

Answer:

There are x stickers in each pack and 2 packs are bought so the total number of stickers bought are x × 2 = 2x. He also bought 8 more stickers, so the total number of stickers bought are 2x + 8.

Expand the expression: 2(4 + x) = 8 + 2x = 2x + 8. Yes, the 2 expressions are equivalent.

**Your Turn**

**Combine like terms.**

Question 8.

8y – 3y = ___________

Answer:

Combine like terms

8y – 3y 8y and 3y are like terms

8y – 3y = y(8 – 3) Distributive Property

= y(5) Subtract inside the parentheses

= 5y Commutative Property of Multiplication

5y Final Solution

Question 9.

6x^{2} + 4(x^{2} – 1) = ______

Answer:

Given expression:

6x^{2} + 4(x^{2} – 1)

Apply distributive property to expand the parentheses:

= 6x^{2} + 4x^{2} – 4

Perform the indicated operation between like terms to combine like terms, therefore:

= 10x^{2} – 4

6x^{2} + 4(x^{2} – 1)= 10x^{2} – 4

Question 10.

4a^{5} – 2a^{5} + 4b + b = ___

Answer:

Given expression:

4a^{5} – 2a^{5} + 4b + b

Perform the indicated operation between like terms to combine like terms, therefore:

= 2a^{5} – 5b

4a^{5} – 2a^{5} + 4b + b = 2a^{5} + 5b

Question 11.

8m + 14 – 12 + 4n = ____

Answer:

Given expression:

8m + 14 – 12 + 4n

Perform the indicated operation between like terms to combine like terms, therefore:

= 8m – 2 – 4n

8m + 14 – 12 + 4n = 8m + 2 + 4n

**Texas Go Math Grade 6 Lesson 11.3 Guided Practice Answer Key**

Question 1.

Evaluate each of the expressions in the list for y 5. Then, draw lines to match the expressions in List A with their equivalent expressions in List B.

Answer:

Determine the equivalent expressions.

The equivalent expressions are:

a. 4 + 4y and 4 (y + 1) Distributive Property of Multiplication over Addition

b. 4 (y – 1) and 4y – 4 Distributive Property of Multiplication over Subtraction

c. 4y + 1 and 1 + 4y Commutative Property of Addition

Question 2.

Determine if the expressions are equivalent by comparing the models. (Explore Activity 2)

Answer:

The expressions are not equivalent based on the tiles shown. In x – 4, there are 1 tile for x and 4 tiles for -1 while in 2 (x – 2), there are 2 tiles for x and 4 tiles for -1.

x – 4 ≠ 2x – 4 by applying distributive property of multiplication over subtraction

The given expressions are not equivalent based on the models indicated.

For each expression, use a property to write an equivalent expression. Tell which property you used.

Question 3.

ab = ______________________

Answer:

Given expression:

ab = ba

According to commutative property of multiplication

ab = ba according to commutative property of multiplication.

Question 4.

5(3x – 2) = ___

Answer:

The operation in the expression is Multiplication.

You can use the Distributive Property to write an equivalent expression: 5(3x – 2) = 15x – 10 (Final solution)

15x – 10

**Use the properties of operations to determine if each pair of expressions is equivalent. (Example 2)**

Question 5.

\(\frac{1}{2}\)(4 – 2x); 2 – 2x ___________

Answer:

Given expression:

\(\frac{1}{2}\)(4 – 2x)

Apply distributive property of multiplication to expand the parentheses:

= \(\frac{1}{2}\)(4) + \(\frac{1}{2}\)(-2x)

Expand:

= 2 – x ≠ 2 – 2x

\(\frac{1}{2}\)(4 – 2x); ≠ 2 – 2x

Question 6.

\(\frac{1}{2}\)(6x – 2); 3 – x _____

Answer:

Given expression:

\(\frac{1}{2}\)(6x – 2)

Apply distributive property of multiplication to expand the parentheses:

= \(\frac{1}{2}\)(6x) + \(\frac{1}{2}\)(-2)

Expand:

= 3x – 1 ≠ 3 – x

\(\frac{1}{2}\)(6x – 2); 3 – x ≠ 3x – 1

**Combine like terms. (Example 3)**

Question 7.

32y + 12y _____________

Answer:

Combine like terms

32y + 12 32y and 12y are like terms.

32y + 12y = y(32 + 12) Distributive Property

= y(44) Add inside the parentheses.

= 44y Commutative Property of Multiplication

32y + 12y = 44y Final Solution

32y + 12y = 44y

Question 8.

12 + 3x – x – 12 = ___

Answer:

Combine like terms

12 + 3x – x – 12

12 + 3x – x – 12 = 2x Distributive Property

12 + 3x – x – 12 = 2x Final solution

**Essential Question Check-In**

Question 9.

Describe two ways to write equivalent algebraic expressions.

Answer:

The condensed form of an algebraic expression is by using parentheses, for example: 4(x + 3). Distributive property of multiplication can be applied here to expand it, therefore= 4x + 12. These 2 expressions are equal to each other.

**Texas Go Math Grade 6 Lesson 11.3 Independent Practice Answer Key**

**For each expression, use a property to write an equivalent expression. Tell which property you used.**

Question 10.

cd = ___

Answer:

Given expression:

cd = dc

According to commutative property of multiplication.

cd = dc according to commutative property of multiplication.

Question 11.

x + 13 = ___

Answer:

The operation in the expression is Addition.

You can use the Commutative Property of Addition to write an equivalent expression: x + 13 = 13 + x (Final solution)

13 + x

Question 12.

4(2x – 3) = ___

Answer:

Given expression:

4(2x – 3) = 8x – 12

According to distributive property of multiplication

4(2x – 3) = 8x – 12 according to distributive property of multiplication.

Question 13.

2 + (a + b) = ___

Answer:

The operation in the expression is Addition.

You can use the Associative Property of Addition to write an equivalent expression: 2 + (a + b) = (2 + a) + b (Final solution)

(2 + a) + b

Question 14.

Draw algebra tile models to prove that 4 + 8x and 4(2x + 1) are equivalent.

Answer:

Algebra tile models for the given expression.

The expressions are equivalent as shown on the tiles. In 4 + 8, there are 4 tiles for +1 and 8 tiles for x which is similar to the tiles of 4(2x + 1).

The expressions are equivalent based on the diagram.

Combine like terms.

Question 15.

7x^{4} – 5x^{4} = ___________________

Answer:

7x^{4} – 5×4^{4} = x^{4}(7 – 5) ← Distributive Property

= x^{4}(2) ← Subtract inside the parentheses

= 2x^{4} ← Commutative Property of Multiplication

The final result is 2x^{4}

Question 16.

32y + 5y = ________

Answer:

Given expression:

32y + 5y =

Perform the indicated operation between like terms to combine the like terms, therefore:

= 37y

32y + 5y = 37y

Question 17.

6b + 7b – 10 = ___

Answer:

Combine like terms

6b + 7b – 10 32y and 5y are like terms.

6b + 7b – 10 = 13b – 10 Distributive Property

13b – 10 Final Solution

Question 18.

2x + 3x + 4 = ___

Answer:

Combine like terms

2x + 3x + 4

2x + 3x + 4 = 5x + 4 Distributive Property

5x + 4 Final Solution

Question 19.

y + 4 + 3(y + 2) = ____

Answer:

Combine like terms

y + 4 + 3(y + 2)

y + 4 + 3(y + 2) = y + 4 + 3y + 6 Distributive Property

= y + 3y + 4 + 6 Commutative Property of Addition

= 4y + 10 Add

y + 4 + 3(y + 2) = 4y + 10

4y + 10 Final Solution

Question 20.

7a^{2} – a^{2} + 16 = ____

Answer:

Given expression:

7a^{2} – a^{2} + 16

Perform the indicated operation between like terms to combine the like terms, therefore:

= 6a^{2} + 16

7a^{2} – a^{2} + 16 = 6a^{2} + 16

Question 21.

3y^{2} + 3(4y^{2} – 2) = ____

Answer:

Given expression:

3y^{2} + 3(4y^{2} – 2)

Apply distributive property to expand the parentheses:

= 3y^{2} + 12y^{2} – 6

Perform the indicated operation between like terms to combine the like terms, therefore:

= 15y^{2} – 6

3y^{2} + 3(4y^{2} – 2) = 15y^{2} – 6

Question 22.

z^{2} + z + 4z^{3} + 4z^{2} = ___

Answer:

Combine like terms

z^{2} + z + 4z^{3} + 4z^{2}

z^{2} + z + 4z^{3} + 4z^{2} = 4z^{3} + 4z^{2} + z^{2} + z Comutative Property of Addition

= 4z^{3} + 5z^{2} + z Distributive Property

z^{2} + z + 4z^{3} + 4z^{2} = 4z + 5z^{2} + z

4z^{3} + 5z^{2} + z Final Solution

Question 23.

0.5(x^{4} – 3) + 12 = ____

Answer:

Combine like terms

0.5(x^{4} – 3) + 12

0.5(x^{4} – 3) + 12 = 0.5x^{4} – 1.5 + 12 Distributive Property

= 0.5x^{4} + 10.5 Add

0.5(x^{4} – 3) + 12 = 0.5x^{4} + 10.5

0.5x^{4} + 10.5 Final Solution

Question 24.

\(\frac{1}{4}\)(16 + 4p) = ____

Answer:

Given expression:

\(\frac{1}{4}\)(16 + 4p)

Apply distributive property to expand the parentheses:

= \(\frac{1}{4}\)(16) + \(\frac{1}{4}\)(4p)

Expand:

= 4 + p

\(\frac{1}{4}\)(16 + 4p) = 4 + p

Question 25.

**Justify Reasoning** Is 3x + 12 – 2x equivalent to x + 12? Use two properties of operations to justify your answer.

Answer:

Determine if the expressions are equivalent.

= 3x – 2x + 12 commutative property of addition

= x + 12 combine like terms by subtracting the coefficient of the same variables

= 3 + 12 – 2x associative property of addition

= (3x – 2x) + 12 subtract the numbers inside the parenthesis

= x + 12

The given expressions are equivalent when commutative or associative property of addition is applied.

Question 26.

William earns $13 an hour working at a movie theater. Last week he worked h hours at the concession stand and three times as many hours at the ticket counter. Write and simplify an expression for the amount of money William earned last week.

Answer:

Last week he worked h hours at the concession stand and three times as many hours at the ticket counter This implies that he worked for 3 × h = 3h hours at the ticket counter The total number of hours worked are therefore: h + 3h = 4h.

His hourly rate at the theater is $13 so he earned $13 × 4h = $52h last week.

Question 27.

**Multiple Representations** Use the information in the table to write and simplify an expression to find the total weight of the medals won by the top medal-winning nations in the 2012 London Olympic Games. The three types of medals have different weights.

Answer:

Let g be the weight of a gold medal, s be the weight of a silver medal and b be the weight of a bronze medal.

The total weight of gold medals won by the 3 countries is g(46 + 38 + 29) = 113g. The total weight of silver medals won by the 3 countries is s(29 + 27 + 17) = 73s and the total weight of bronze medals won by the 3 countries is b(29 + 23 + 19) = 71b.

Their total sum is 113g + 73s + 71b.

Write an expression for the perimeters of each given figure. Simplify the expressions.

Question 28.

_____________

Answer:

Perimeter of a figure is the sum of its sides. Here 2 opposite sides are equal in length so the perimeter of the given figure is equal to 2(6) + 2(3x – 1):

Apply distributive property to expand the parentheses:

= 12 + 6x – 2

Perform the indicated operation between like terms to combine the like terms, therefore:

= 6x + 10

Perimeter of the figure shown is 6x + 10 millimeters.

Question 29.

___________

Answer:

Perimeter of a figure is the sum of its sides. Here 2 opposite sides are equal in Length and 4 other sides are also equal so the perimeter of the given figure is equal to 2(10.2) + 4(x + 4):

Apply distributive property to expand the parentheses:

= 20.4 + 4x + 16

Perform the indicated operation between like terms to combine the like terms, therefore:

= 4x + 36.4

Perimeter of the figure shown is 4x + 36.4 inches.

**Texas Go Math Grade 6 Lesson 11.3 H.O.T. Focus On Higher Order Thinking Answer Key**

Question 30.

**Problem Solving** Examine the algebra tile model.

a. Write two equivalent expressions for the model. ____

Answer:

The model shown represents 4 tiles of +1 and 6 tiles of -x. Therefore, the equivalent expressions for the model are 4 – 6x or 2 (2 – 3x).

The equivalent expressions are 4 – 6x and 2 (2 – 3)

b. What If? Suppose a third row of tiles identical to the ones above is added to the model. How does that change the two expressions?

Answer:

If a third row will be added, the expression will be 6 – 9x or 3 (2 – 3x). Since there will be 6 tiles of +1 and 9 tiles of -x.

The equivalent expressions are 6 – 9x and 3 (2 – 3x)

Question 31.

**Communicate Mathematical Ideas** Write an example of an expression that cannot be simplified, and explain how you know that it cannot be simplified.

Answer:

An example of such an expression is 8x + 100. It can be seen that the expression consists of 2 terms that are no like terms so the expression can no longer be simplified.

Question 32.

**Problem Solving** Write an expression that is equivalent to 8(2y + 4) that can be simplified.

Answer:

Given expression:

8(2y + 4)

Apply distributive property to expand the parentheses:

= 8(2y) + 8(4)

Simplify:

= 16y + 32

This expression can be broken down to form an expression with some like term that is equivalent to the given expression, therefore:

= 10y + 6y + 30 + 2

Note that there can be many answers to this question.