SOLUTION: Linear Equation Practice 100 Problems: Math (the answers ... - Free Printable

The image shows a worksheet titled "LINEAR EQUATIONS PRACTICE," which contains numerous linear equations to solve. Below, I will explain the general approach to solving linear equations and provide examples for a few of the problems.

General Steps to Solve Linear Equations:

1. Simplify both sides: Remove parentheses, combine like terms, and simplify expressions.
2. Isolate the variable: Use addition, subtraction, multiplication, or division to isolate the variable on one side of the equation.
3. Solve for the variable: Perform any necessary operations to find the value of the variable.
4. Verify the solution: Substitute the solution back into the original equation to ensure it satisfies the equation.

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Example Solutions:

#### Problem 1: \( 4x = 4 \)
1. Divide both sides by 4:
\[
x = \frac{4}{4} = 1
\]
2. Solution: \( x = 1 \)

#### Problem 2: \( x + 6 = -7 \)
1. Subtract 6 from both sides:
\[
x = -7 - 6 = -13
\]
2. Solution: \( x = -13 \)

#### Problem 3: \( x - 4 = 7 \)
1. Add 4 to both sides:
\[
x = 7 + 4 = 11
\]
2. Solution: \( x = 11 \)

#### Problem 4: \( \frac{x}{3} = -9 \)
1. Multiply both sides by 3:
\[
x = -9 \cdot 3 = -27
\]
2. Solution: \( x = -27 \)

#### Problem 5: \( 2x + 4 = 8 \)
1. Subtract 4 from both sides:
\[
2x = 8 - 4 = 4
\]
2. Divide both sides by 2:
\[
x = \frac{4}{2} = 2
\]
3. Solution: \( x = 2 \)

#### Problem 6: \( 14 = 3 + 2x \)
1. Subtract 3 from both sides:
\[
14 - 3 = 2x \implies 11 = 2x
\]
2. Divide both sides by 2:
\[
x = \frac{11}{2}
\]
3. Solution: \( x = \frac{11}{2} \)

#### Problem 7: \( 8x - 3 = -19 \)
1. Add 3 to both sides:
\[
8x = -19 + 3 = -16
\]
2. Divide both sides by 8:
\[
x = \frac{-16}{8} = -2
\]
3. Solution: \( x = -2 \)

#### Problem 8: \( 6 - x = 9 \)
1. Subtract 6 from both sides:
\[
-x = 9 - 6 = 3
\]
2. Multiply both sides by -1:
\[
x = -3
\]
3. Solution: \( x = -3 \)

#### Problem 9: \( -x = -12 \)
1. Multiply both sides by -1:
\[
x = 12
\]
2. Solution: \( x = 12 \)

#### Problem 10: \( 3(x - 2) = 6 \)
1. Distribute the 3:
\[
3x - 6 = 6
\]
2. Add 6 to both sides:
\[
3x = 12
\]
3. Divide both sides by 3:
\[
x = \frac{12}{3} = 4
\]
4. Solution: \( x = 4 \)

#### Problem 37: \( \frac{2}{8} + \frac{3}{4} = \frac{w}{5} \)
1. Simplify the left-hand side:
\[
\frac{2}{8} = \frac{1}{4}, \quad \text{so } \frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1
\]
2. The equation becomes:
\[
1 = \frac{w}{5}
\]
3. Multiply both sides by 5:
\[
w = 5
\]
4. Solution: \( w = 5 \)

#### Problem 68: \( -\frac{9}{5}x = -45 \)
1. Multiply both sides by \(-\frac{5}{9}\):
\[
x = -45 \cdot \left(-\frac{5}{9}\right) = \frac{225}{9} = 25
\]
2. Solution: \( x = 25 \)

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Final Answer:

The solutions to the problems are as follows (only a few are shown here; you can apply the same method to solve all):

- Problem 1: \( x = 1 \)
- Problem 2: \( x = -13 \)
- Problem 3: \( x = 11 \)
- Problem 4: \( x = -27 \)
- Problem 5: \( x = 2 \)
- Problem 6: \( x = \frac{11}{2} \)
- Problem 7: \( x = -2 \)
- Problem 8: \( x = -3 \)
- Problem 9: \( x = 12 \)
- Problem 10: \( x = 4 \)
- Problem 37: \( w = 5 \)
- Problem 68: \( x = 25 \)

For the complete set of solutions, follow the same steps for each problem.

\boxed{\text{See above for detailed solutions.}}