Question

Steps to Solve a Multi-Step Equation Practice

Answer 1

Solving multi-step equations can be broken down into a series of steps. Here’s a general approach to help you practice:

### Steps to Solve a Multi-Step Equation

1. **Simplify Both Sides**:
- If there are parentheses, use the distributive property to eliminate them.
- Combine like terms on each side of the equation.

2. **Get All Variable Terms on One Side**:
- Use addition or subtraction to move the variable terms to one side of the equation and the constant terms to the other.

3. **Isolate the Variable**:
- If there are any coefficients (numbers multiplied by the variable), divide or multiply both sides of the equation by that number to get the variable by itself.

4. **Check Your Solution**:
- Substitute your solution back into the original equation to verify that both sides are equal.

### Example Practice Problems

Here are a few practice problems along with their solutions:

#### Problem 1:
Solve for \( x \):
\[ 2(x + 3) - 4 = 8 \]

**Solution Steps**:
1. Distribute:
\[ 2x + 6 - 4 = 8 \]
2. Simplify:
\[ 2x + 2 = 8 \]
3. Move constant terms:
\[ 2x = 6 \]
4. Isolate \( x \):
\[ x = 3 \]

#### Problem 2:
Solve for \( y \):
\[ 3y - 5 = 2(y + 1) \]

**Solution Steps**:
1. Distribute:
\[ 3y - 5 = 2y + 2 \]
2. Get variable terms on one side:
\[ 3y - 2y = 2 + 5 \]
3. Simplify:
\[ y = 7 \]

#### Problem 3:
Solve for \( z \):
\[ 4(z - 2) + 6 = 2(z + 10) \]

**Solution Steps**:
1. Distribute:
\[ 4z - 8 + 6 = 2z + 20 \]
2. Combine like terms:
\[ 4z - 2 = 2z + 20 \]
3. Get variable terms on one side:
\[ 4z - 2z = 20 + 2 \]
4. Simplify:
\[ 2z = 22 \]
5. Isolate \( z \):
\[ z = 11 \]

### Additional Practice Problems
Try solving these on your own:
1. \( 5(x - 2) + 4 = 2(x + 8) \)
2. \( 6 - 2(3y - 1) = 5y + 1 \)
3. \( 2(3z + 4) = 12 + 6z \)

### Tips
- Always perform the same operation on both sides of the equation.
- Double-check your math as you go.
- Practice is key! The more multi-step equations you solve, the more confident you will become.

Feel free to ask for solutions to the additional practice problems or any specific questions!