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

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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.

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