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## McGraw-Hill Math Grade 7 Answer Key Lesson 17.4 Solving Equations and Inequalities by Multiplication and Division

**Exercises**

**SOLVE**

Question 1.

2y + 15 = 25

Answer:

Given equation is 2y + 15 = 25

Subtract 15 from both sides of the equation.

2y + 15 – 15 = 25 – 15

2y = 10

To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.

2y/2 = 10/2

**y = 5
**The value of y is equal to 5.

Question 2.

5 + 5p < 70

Answer:

Given inequality is 5 + 5p < 70

Subtract 5 from both sides of the inequality.

5 + 5p – 5 < 70 – 5

5p < 65

To solve above multiplication inequality we need to divide both sides of the inequality by 5 to find p.

5p/5 < 65/5

**p < 13
**The value of p is less than 13.

Question 3.

8c + 8 > 224

Answer:

Given inequality is 8c + 8 > 224

Subtract 8 from both sides of the inequality.

8c + 8 – 8 > 224 – 8

8c > 216

To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find c.

8c/8 > 216/8

**c > 27
**The value of c is greater than 27.

Question 4.

17 + \(\frac{w}{3}\) = 45

Answer:

Given equation is 17 + \(\frac{w}{3}\) = 45

Subtract 17 from both sides of the equation.

17 + \(\frac{w}{3}\) – 17= 45 – 17

\(\frac{w}{3}\) = 28

To solve above division equation we need to multiply both sides of the equation by 3 to find w.

\(\frac{w}{3}\) x 3 = 28 x 3

**w = 84
**The value of w is equal to 84.

Question 5.

34 = 10 + 4q

Answer:

Given equation is 34 = 10 + 4q

Subtract 10 from both sides of the equation.

34 – 10 = 10 + 4q -10

24 = 4q

To solve above multiplication equation we need to divide both sides of the equation by 4 to find q.

24/4 = 4q/4

**6 = q
**The value of q is equal to 6.

Question 6.

42 = 7 + \(\frac{z}{5}\)

Answer:

Given equation is 42 = 7 + \(\frac{z}{5}\)

Subtract 7 from both sides of the equation.

42 – 7 = 7 + \(\frac{z}{5}\) – 7

35 = \(\frac{z}{5}\)

To solve above division equation we need to multiply both sides of the equation by 5 to find z.

35 x 5= \(\frac{z}{5}\) x 5

**175 = z
**The value of z is equal to 175.

Question 7.

232 ≤ 8 + 8x

Answer:

Given inequality is 232 ≤ 8 + 8x

Subtract 8 from both sides of the inequality.

232 – 8 ≤ 8 + 8x – 8

224 ≤ 8x

To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find x.

224/8 ≤ 8x/8

**28 ≤ x
**The value of x is greater than or equal to 28.

Question 8.

63 = 3 + 4g

Answer:

Given equation is 63 = 3 + 4g

Subtract 3 from both sides of the equation.

63 – 3 = 3 + 4g – 3

60 = 4g

To solve above multiplication equation we need to divide both sides of the equation by 4 to find g.

60/4 = 4g/4

**15 = g
**The value of g is equal to 15.

Question 9.

12 = \(\frac{g}{9}\)

Answer:

Given equation is 12 = \(\frac{g}{9}\)

To solve above division equation we need to multiply both sides of the equation by 9 to find g.

12 x 9 = \(\frac{g}{9}\) x 9

**108 = g
**The value of g is equal to 108.

Question 10.

3k + 5 > 56

Answer:

Given inequality is 3k + 5 > 56

Subtract 5 from both sides of the inequality.

3k + 5 – 5 > 56 – 5

3k > 51

To solve above multiplication inequality we need to divide both sides of the inequality by 3 to find k.

3k/3 > 51/3

**K > 17
**The value of k is greater than 17.

Question 11.

49 ≥ 10 + \(\frac{p}{5}\)

Answer:

Given inequality is 49 ≥ 10 + \(\frac{p}{5}\)

Subtract 10 from both sides of the inequality.

49 – 10 ≥ 10 + \(\frac{p}{5}\) – 10

39 ≥ \(\frac{p}{5}\)

To solve above division equation we need to multiply both sides of the equation by 5 to find p.

39 x 5 ≥ \(\frac{p}{5}\) x 5

**195 ≥ p
**The value of p is less than or equal to 195.

Question 12.

2y + 5 = 74

Answer:

Given equation is 2y + 5 = 74

Subtract 5 from both sides of the equation.

2y + 5 – 5 = 74 – 5

2y = 69

To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.

2y/2 = 69/2

**y = 34.5
**The value of y is equal to 34.5.

Question 13.

8d + 130 = 210

Answer:

Given equation is 8d + 130 = 210

Subtract 130 from both sides of the equation.

8d + 130 – 130 = 210 – 130

8d = 80

To solve above multiplication equation we need to divide both sides of the equation by 8 to find d.

8d/8 = 80/8

**d = 10
**The value of d is equal to 10.

Question 14.

33 + \(\frac{1}{3}\)c ≤ 66

Answer:

Given inequality is 33 + \(\frac{1}{3}\)c ≤ 66

Subtract 33 from both sides of the inequality.

33 + \(\frac{1}{3}\)c – 33 ≤ 66 – 33

\(\frac{1}{3}\)c ≤ 33

To solve above division inequality we need to multiply both sides of the inequality by 3 to find c.

\(\frac{1}{3}\)c x 3 ≤ 33 x 3

**c ≤ 99
**The value of c is less than or equal to 99.