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!