Question

solve each equation.

1. $3b + 6b = 45$
2. $4y - 10y = 42$
3. $-8r + 10r = 20$
4. $15d - 11d = -28$
5. $7a + 6a - a = 48$
6. $2w - 9w + 10w = -27$
7. $5m - 14m + 2m = 35$
8. $6p - 13p - 10p + 2p = -45$
9. $-4c - c - 8c + 3c = -80$
10. $29g - 5g - 11g - 20g = 63$

Explanation:

Step1: Combine like terms

$3b + 6b = 9b$

Step2: Isolate $b$

$b = \frac{45}{9} = 5$

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Step1: Combine like terms

$4y - 10y = -6y$

Step2: Isolate $y$

$y = \frac{42}{-6} = -7$

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Step1: Combine like terms

$-8r + 10r = 2r$

Step2: Isolate $r$

$r = \frac{20}{2} = 10$

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Step1: Combine like terms

$15d - 11d = 4d$

Step2: Isolate $d$

$d = \frac{-28}{4} = -7$

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Step1: Combine like terms

$7a + 6a - a = 12a$

Step2: Isolate $a$

$a = \frac{48}{12} = 4$

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Step1: Combine like terms

$2w - 9w + 10w = 3w$

Step2: Isolate $w$

$w = \frac{-27}{3} = -9$

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Step1: Combine like terms

$5m - 14m + 2m = -7m$

Step2: Isolate $m$

$m = \frac{35}{-7} = -5$

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Step1: Combine like terms

$6p - 13p - 10p + 2p = -15p$

Step2: Isolate $p$

$p = \frac{-45}{-15} = 3$

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Step1: Combine like terms

$-4c - c - 8c + 3c = -10c$

Step2: Isolate $c$

$c = \frac{-80}{-10} = 8$

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Step1: Combine like terms

$29g - 5g - 11g - 20g = -7g$

Step2: Isolate $g$

$g = \frac{63}{-7} = -9$

Answer:

1. $b=5$
2. $y=-7$
3. $r=10$
4. $d=-7$
5. $a=4$
6. $w=-9$
7. $m=-5$
8. $p=3$
9. $c=8$
10. $g=-9$