Directions: Solve each equation for the variable. SHOW YOUR WORK FOR CREDIT! 25. $$ 4 a-9=7 a+12 $$ 26. $$ 13 b=6 b+14 $$ 27. $$ 3(5 c-4)=8 c+2 $$ 28. $$ 2 d+18=12-6(d+7) $$ 29. $$ 8(e-5)=2(3 e-8) $$ 30. $$ f-8=6+3 f $$ 31. $$ g+4 g=2 g-15 $$ 32. $$ -3(2 h-4)=20-4 h $$ 33. $$ -5 i-3=-43 $$ 34. $$ j-(5-3 j)=7 j+4 $$ 35. $$ 8 k-15=4 k+13 $$ 36. $$ 2(5-3 r)=-4 r-16 $$

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UpStudy AI · Accepted Answer

**25.** Solve $$ 4a - 9 = 7a + 12 $$.  
Subtract $$ 4a $$ from both sides:  
$$
-9 = 3a + 12
$$  
Subtract 12 from both sides:  
$$
-21 = 3a
$$  
Divide by 3:  
$$
a = -7
$$

**26.** Solve $$ 13b = 6b + 14 $$.  
Subtract $$ 6b $$ from both sides:  
$$
7b = 14
$$  
Divide by 7:  
$$
b = 2
$$

**27.** Solve $$ 3(5c - 4) = 8c + 2 $$.  
Distribute on the left-hand side:  
$$
15c - 12 = 8c + 2
$$  
Subtract $$ 8c $$ from both sides:  
$$
7c - 12 = 2
$$  
Add 12 to both sides:  
$$
7c = 14
$$  
Divide by 7:  
$$
c = 2
$$

**28.** Solve $$ 2d + 18 = 12 - 6(d+7) $$.  
Distribute on the right-hand side:  
$$
2d + 18 = 12 - 6d - 42
$$  
Combine like terms on the right:  
$$
2d + 18 = -6d - 30
$$  
Add $$ 6d $$ to both sides:  
$$
8d + 18 = -30
$$  
Subtract 18 from both sides:  
$$
8d = -48
$$  
Divide by 8:  
$$
d = -6
$$

**29.** Solve $$ 8(e-5) = 2(3e-8) $$.  
Distribute both sides:  
$$
8e - 40 = 6e - 16
$$  
Subtract $$ 6e $$ from both sides:  
$$
2e - 40 = -16
$$  
Add 40 to both sides:  
$$
2e = 24
$$  
Divide by 2:  
$$
e = 12
$$

**30.** Solve $$ f - 8 = 6 + 3f $$.  
Subtract $$ 3f $$ from both sides:  
$$
f - 3f - 8 = 6
$$  
Simplify:  
$$
-2f - 8 = 6
$$  
Add 8 to each side:  
$$
-2f = 14
$$  
Divide by -2:  
$$
f = -7
$$

**31.** Solve $$ g + 4g = 2g - 15 $$.  
Combine like terms on the left:  
$$
5g = 2g - 15
$$  
Subtract $$ 2g $$ from both sides:  
$$
3g = -15
$$  
Divide by 3:  
$$
g = -5
$$

**32.** Solve $$ -3(2h - 4) = 20 - 4h $$.  
Distribute the left-hand side:  
$$
-6h + 12 = 20 - 4h
$$  
Add $$ 6h $$ to both sides:  
$$
12 = 20 + 2h
$$  
Subtract 20 from both sides:  
$$
-8 = 2h
$$  
Divide by 2:  
$$
h = -4
$$

**33.** Solve $$ -5i - 3 = -43 $$.  
Add 3 to both sides:  
$$
-5i = -40
$$  
Divide by -5:  
$$
i = 8
$$

**34.** Solve $$ j - (5 - 3j) = 7j + 4 $$.  
Distribute the negative sign:  
$$
j - 5 + 3j = 7j + 4
$$  
Combine like terms:  
$$
4j - 5 = 7j + 4
$$  
Subtract $$ 4j $$ from both sides:  
$$
-5 = 3j + 4
$$  
Subtract 4 from both sides:  
$$
-9 = 3j
$$  
Divide by 3:  
$$
j = -3
$$

**35.** Solve $$ 8k - 15 = 4k + 13 $$.  
Subtract $$ 4k $$ from both sides:  
$$
4k - 15 = 13
$$  
Add 15 to both sides:  
$$
4k = 28
$$  
Divide by 4:  
$$
k = 7
$$

**36.** Solve $$ 2(5-3r) = -4r - 16 $$.  
Distribute on the left-hand side:  
$$
10 - 6r = -4r - 16
$$  
Add $$ 6r $$ to both sides:  
$$
10 = 2r - 16
$$  
Add 16 to both sides:  
$$
26 = 2r
$$  
Divide by 2:  
$$
r = 13
$$
**25.** $$ a = -7 $$ **26.** $$ b = 2 $$ **27.** $$ c = 2 $$ **28.** $$ d = -6 $$ **29.** $$ e = 12 $$ **30.** $$ f = -7 $$ **31.** $$ g = -5 $$ **32.** $$ h = -4 $$ **33.** $$ i = 8 $$ **34.** $$ j = -3 $$ **35.** $$ k = 7 $$ **36.** $$ r = 13 $$

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