Solving Linear Equations - Annie Wadzinski - Canva - Free Printable

Here are the step-by-step solutions for each equation on the worksheet.

1. 2(x + 3) - 5(x - 1) = 8
* Distribute the numbers outside the parentheses:
$2x + 6 - 5x + 5 = 8$
* Combine like terms ($2x - 5x$ and $6 + 5$):
$-3x + 11 = 8$
* Subtract 11 from both sides:
$-3x = -3$
* Divide by -3:
x = 1

2. 1.5(2p - 0.5) - 0.5p = 1.25
* Distribute the 1.5:
$3p - 0.75 - 0.5p = 1.25$
* Combine like terms ($3p - 0.5p$):
$2.5p - 0.75 = 1.25$
* Add 0.75 to both sides:
$2.5p = 2$
* Divide by 2.5:
p = 0.8

3. 3(2y + 1) + 2(3y - 4) = 19
* Distribute the numbers:
$6y + 3 + 6y - 8 = 19$
* Combine like terms ($6y + 6y$ and $3 - 8$):
$12y - 5 = 19$
* Add 5 to both sides:
$12y = 24$
* Divide by 12:
y = 2

4. 2b + 0.5b - 3 = 5
* Combine like terms ($2b + 0.5b$):
$2.5b - 3 = 5$
* Add 3 to both sides:
$2.5b = 8$
* Divide by 2.5:
b = 3.2

5. 6 = 2(x + 3) + 0.5x
* Distribute the 2:
$6 = 2x + 6 + 0.5x$
* Combine like terms ($2x + 0.5x$):
$6 = 2.5x + 6$
* Subtract 6 from both sides:
$0 = 2.5x$
* Divide by 2.5:
x = 0

6. -5(3g + 2) - 4g = 9
* Distribute the -5 (be careful with signs!):
$-15g - 10 - 4g = 9$
* Combine like terms ($-15g - 4g$):
$-19g - 10 = 9$
* Add 10 to both sides:
$-19g = 19$
* Divide by -19:
g = -1

7. 4m + 3m - 13 = 15
* Combine like terms ($4m + 3m$):
$7m - 13 = 15$
* Add 13 to both sides:
$7m = 28$
* Divide by 7:
m = 4

8. -1 = 4(2y + 5) - 3(4y - 3)
* Distribute the 4 and the -3:
$-1 = 8y + 20 - 12y + 9$
* Combine like terms ($8y - 12y$ and $20 + 9$):
$-1 = -4y + 29$
* Subtract 29 from both sides:
$-30 = -4y$
* Divide by -4:
y = 7.5

Final Answer:
1. x = 1
2. p = 0.8
3. y = 2
4. b = 3.2
5. x = 0
6. g = -1
7. m = 4
8. y = 7.5