Question

directions: solve each equation for the variable. show your work for credit

1. -5 = 6d - 7d + 4
2. 4e - 4 = e - 4
3. -7f + 6 = 116 + 3f
4. 4 + 2g + 5g = -66
5. 5h + 3 = 3h + 11
6. 5i + 4 = 14 + 4i
7. 4j + 26 = 50 + 6j
8. 2k + 36 = 6k - 12
9. l + 21 = -l + 87
10. 3q + 7 = 7q - 13
11. 21 - r = -87 + 2r
12. 2s - 54 = -s + 21

Explanation:

Problem 16:

Step1: Combine like terms

$4 + 7g = -66$

Step2: Subtract 4 from both sides

$7g = -66 - 4$
$7g = -70$

Step3: Divide by 7

$g = \frac{-70}{7}$

Problem 17:

Step1: Subtract 3h from both sides

$2h + 3 = 11$

Step2: Subtract 3 from both sides

$2h = 11 - 3$
$2h = 8$

Step3: Divide by 2

$h = \frac{8}{2}$

Problem 18:

Step1: Subtract 4i from both sides

$i + 4 = 14$

Step2: Subtract 4 from both sides

$i = 14 - 4$

Problem 19:

Step1: Subtract 4j from both sides

$26 = 50 + 2j$

Step2: Subtract 50 from both sides

$2j = 26 - 50$
$2j = -24$

Step3: Divide by 2

$j = \frac{-24}{2}$

Problem 20:

Step1: Subtract 2k from both sides

$36 = 4k - 12$

Step2: Add 12 to both sides

$4k = 36 + 12$
$4k = 48$

Step3: Divide by 4

$k = \frac{48}{4}$

Problem 21:

Step1: Add L to both sides

$2L + 21 = 87$

Step2: Subtract 21 from both sides

$2L = 87 - 21$
$2L = 66$

Step3: Divide by 2

$L = \frac{66}{2}$

Problem 22:

Step1: Subtract 3q from both sides

$7 = 4q - 13$

Step2: Add 13 to both sides

$4q = 7 + 13$
$4q = 20$

Step3: Divide by 4

$q = \frac{20}{4}$

Problem 23:

Step1: Add r to both sides

$21 = -87 + 3r$

Step2: Add 87 to both sides

$3r = 21 + 87$
$3r = 108$

Step3: Divide by 3

$r = \frac{108}{3}$

Problem 24:

Step1: Add s to both sides

$3s - 54 = 21$

Step2: Add 54 to both sides

$3s = 21 + 54$
$3s = 75$

Step3: Divide by 3

$s = \frac{75}{3}$

Answer:

1. $g = -10$
2. $h = 4$
3. $i = 10$
4. $j = -12$
5. $k = 12$
6. $L = 33$
7. $q = 5$
8. $r = 36$
9. $s = 25$