Printable worksheet titled "Solving Linear Equations Worksheet" featuring eight problems for students to solve, including equations with variables, parentheses, and fractions.

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

1) $2(m + 6) = 48$
* Divide both sides by 2:
$m + 6 = 24$
* Subtract 6 from both sides:
$m = 18$

2) $8x + 9 - 3x = 8 + 4x + 5$
* Combine like terms on both sides ($8x - 3x$ on the left, $8 + 5$ on the right):
$5x + 9 = 4x + 13$
* Subtract $4x$ from both sides:
$x + 9 = 13$
* Subtract 9 from both sides:
$x = 4$

3) $8a - (4a + 32) = 16$
* Distribute the negative sign into the parentheses:
$8a - 4a - 32 = 16$
* Combine like terms ($8a - 4a$):
$4a - 32 = 16$
* Add 32 to both sides:
$4a = 48$
* Divide by 4:
$a = 12$

4) $-3(x - 1) + 8(x - 3) = 6x + 7 - 5x$
* Distribute the numbers into the parentheses on the left side:
$-3x + 3 + 8x - 24 = 6x + 7 - 5x$
* Combine like terms on both sides:
Left side: $(-3x + 8x) + (3 - 24) \rightarrow 5x - 21$
Right side: $(6x - 5x) + 7 \rightarrow x + 7$
Equation becomes: $5x - 21 = x + 7$
* Subtract $x$ from both sides:
$4x - 21 = 7$
* Add 21 to both sides:
$4x = 28$
* Divide by 4:
$x = 7$

5) $10x + 5(5x - 3) = 5(6x + 4)$
* Distribute the 5s into the parentheses:
$10x + 25x - 15 = 30x + 20$
* Combine like terms on the left side ($10x + 25x$):
$35x - 15 = 30x + 20$
* Subtract $30x$ from both sides:
$5x - 15 = 20$
* Add 15 to both sides:
$5x = 35$
* Divide by 5:
$x = 7$

6) $0.02m + 0.08(8 - m) = 1.78$
* Distribute the $0.08$:
$0.02m + 0.64 - 0.08m = 1.78$
* Combine like terms ($0.02m - 0.08m$):
$-0.06m + 0.64 = 1.78$
* Subtract $0.64$ from both sides:
$-0.06m = 1.14$
* Divide by $-0.06$:
$m = -19$

7) $\frac{1}{3}(10 - 2x) = \frac{1}{3}(8 - 2x)$
* Multiply both sides by 3 to remove the fractions:
$10 - 2x = 8 - 2x$
* Add $2x$ to both sides:
$10 = 8$
* Since 10 does not equal 8, this is a false statement.
No Solution

8) $-14 + 6b + 7 - 2b = 1 + 5b$
* Combine like terms on the left side ($6b - 2b$ and $-14 + 7$):
$4b - 7 = 1 + 5b$
* Subtract $4b$ from both sides:
$-7 = 1 + b$
* Subtract 1 from both sides:
$-8 = b$
$b = -8$

Final Answer:
1) m = 18
2) x = 4
3) a = 12
4) x = 7
5) x = 7
6) m = -19
7) No Solution
8) b = -8