Solving Multi-Step Equations

Multi-step equations require you to perform more than one operation to isolate the variable and solve the equation. These types of equations involve a combination of addition, subtraction, multiplication, division, and sometimes distributing and combining like terms.

Outline

Introduction to Multi-Step Equations
Key Steps in Solving Multi-Step Equations
Examples
Exercises
Homework
Revision Section
Contact Us for Tutoring

Examples of Solving Multi-Step Equations

Example 1:

Solve: \(2x + 3 = 11\)

Step 1: Subtract 3 from both sides: \(2x = 8\)

Step 2: Divide by 2: \(x = 4\)

Example 2:

Solve: \(3(x - 2) = 9\)

Step 1: Distribute the 3: \(3x - 6 = 9\)

Step 2: Add 6 to both sides: \(3x = 15\)

Step 3: Divide by 3: \(x = 5\)

Example 3:

Solve: \(4x - 7 = 13\)

Step 1: Add 7 to both sides: \(4x = 20\)

Step 2: Divide by 4: \(x = 5\)

Example 4:

Solve: \(5(x + 4) = 30\)

Step 1: Distribute the 5: \(5x + 20 = 30\)

Step 2: Subtract 20 from both sides: \(5x = 10\)

Step 3: Divide by 5: \(x = 2\)

Example 5:

Solve: \(\frac{2x}{3} = 8\)

Step 1: Multiply both sides by 3: \(2x = 24\)

Step 2: Divide by 2: \(x = 12\)

Example 6:

Solve: \(7x - 3(x + 2) = 4\)

Step 1: Distribute the -3: \(7x - 3x - 6 = 4\)

Step 2: Combine like terms: \(4x - 6 = 4\)

Step 3: Add 6 to both sides: \(4x = 10\)

Step 4: Divide by 4: \(x = 2.5\)

Exercises

Practice Problems:

Solve: \(3x + 4 = 19\)
Solve: \(2(x - 3) = 12\)
Solve: \(6x - 9 = 15\)
Solve: \(4(x + 2) = 28\)
Solve: \(\frac{3x}{5} = 9\)
Solve: \(8x - 5(x + 3) = 7\)

Homework

Homework Problems:

Solve the following multi-step equations. Show all your work:

Solve: \(5x + 6 = 21\)
Solve: \(4(2x - 1) = 16\)
Solve: \(7x - 2 = 19\)
Solve: \(3(x + 4) = 24\)
Solve: \(\frac{4x}{2} = 14\)
Solve: \(6x - 3(2x + 5) = -12\)

Revision Section

Revise the key concepts of solving multi-step equations by practicing similar problems, reviewing notes, and rewatching the video tutorial embedded below.