Question

like terms
like terms are terms that have the same variables raised to the same powers. you can combine the like terms on each side of an equation to help solve the equation.
lets try it! solve $4h + 3 + 3h - 9 = 36$.
first, find and combine like terms, paying attention to the signs. $4h$ and $3h$ are like terms, and $3$ and $-9$ are like terms. then, use inverse operations to solve.
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$$\begin{align*}4h + 3 + 3h - 9 &= 36\\\\7h - 6 &= 36\\\\7h - 6 + 6 &= 36 + 6\\\\7h &= 42\\\\\\frac{7h}{7} &= \\frac{42}{7}\\\\h &= 6\\end{align*}$$

practice! solve each equation.

1. $-7m + 10m - 8 = 25$
2. $12w - 7 - 3w = -61$
3. $8c - c - 9c + 6 = 40$
4. $9t + 3t - 17t + 4 = 49$
5. $-d + 11 - 4d + 9d = -17$
6. $5g + 2g + g + 6 - 7 = 23$
7. $15 - 8k + 15k - 8 = 42$
8. $-3a + 1 - 4a - 6 + a = 7$

Explanation:

1. Equation: $-7m + 10m - 8 = 25$

Step1: Combine like terms

$3m - 8 = 25$

Step2: Add 8 to both sides

$3m - 8 + 8 = 25 + 8$
$3m = 33$

Step3: Divide by 3

$\frac{3m}{3} = \frac{33}{3}$
$m = 11$

2. Equation: $12w - 7 - 3w = -61$

Step1: Combine like terms

$9w - 7 = -61$

Step2: Add 7 to both sides

$9w - 7 + 7 = -61 + 7$
$9w = -54$

Step3: Divide by 9

$\frac{9w}{9} = \frac{-54}{9}$
$w = -6$

3. Equation: $8c - c - 9c + 6 = 40$

Step1: Combine like terms

$-2c + 6 = 40$

Step2: Subtract 6 from both sides

$-2c + 6 - 6 = 40 - 6$
$-2c = 34$

Step3: Divide by -2

$\frac{-2c}{-2} = \frac{34}{-2}$
$c = -17$

4. Equation: $9t + 3t - 17t + 4 = 49$

Step1: Combine like terms

$-5t + 4 = 49$

Step2: Subtract 4 from both sides

$-5t + 4 - 4 = 49 - 4$
$-5t = 45$

Step3: Divide by -5

$\frac{-5t}{-5} = \frac{45}{-5}$
$t = -9$

5. Equation: $-d + 11 - 4d + 9d = -17$

Step1: Combine like terms

$4d + 11 = -17$

Step2: Subtract 11 from both sides

$4d + 11 - 11 = -17 - 11$
$4d = -28$

Step3: Divide by 4

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

6. Equation: $5g + 2g + g + 6 - 7 = 23$

Step1: Combine like terms

$8g - 1 = 23$

Step2: Add 1 to both sides

$8g - 1 + 1 = 23 + 1$
$8g = 24$

Step3: Divide by 8

$\frac{8g}{8} = \frac{24}{8}$
$g = 3$

7. Equation: $15 - 8k + 15k - 8 = 42$

Step1: Combine like terms

$7k + 7 = 42$

Step2: Subtract 7 from both sides

$7k + 7 - 7 = 42 - 7$
$7k = 35$

Step3: Divide by 7

$\frac{7k}{7} = \frac{35}{7}$
$k = 5$

8. Equation: $-3a + 1 - 4a - 6 + a = 7$

Step1: Combine like terms

$-6a - 5 = 7$

Step2: Add 5 to both sides

$-6a - 5 + 5 = 7 + 5$
$-6a = 12$

Step3: Divide by -6

$\frac{-6a}{-6} = \frac{12}{-6}$
$a = -2$

Answer:

1. $m = 11$
2. $w = -6$
3. $c = -17$
4. $t = -9$
5. $d = -7$
6. $g = 3$
7. $k = 5$
8. $a = -2$