Grade: Grade 7 Subject: Mathematics Unit: Linear Equations SAT: Algebra ACT: Math

Guided Practice: Linear Equations

📖 Learn

This guided practice lesson helps you build confidence solving linear equations. You will work through problems step-by-step with hints and explanations available when needed.

Key Strategies to Remember

  • Isolate the variable: Use inverse operations to get the variable alone on one side
  • Balance the equation: Whatever you do to one side, do to the other
  • Simplify first: Combine like terms before solving
  • Check your answer: Substitute back into the original equation

Order of Operations for Solving

  1. Distribute any multiplication across parentheses
  2. Combine like terms on each side
  3. Move variable terms to one side using addition/subtraction
  4. Move constant terms to the other side
  5. Divide or multiply to isolate the variable

💡 Worked Examples

Example 1: Two-Step Equation

Problem: Solve 3x + 7 = 22

Step 1: Subtract 7 from both sides: 3x + 7 - 7 = 22 - 7

Step 2: Simplify: 3x = 15

Step 3: Divide both sides by 3: x = 5

Check: 3(5) + 7 = 15 + 7 = 22 ✓

Example 2: Variables on Both Sides

Problem: Solve 5x - 3 = 2x + 9

Step 1: Subtract 2x from both sides: 5x - 2x - 3 = 9

Step 2: Simplify: 3x - 3 = 9

Step 3: Add 3 to both sides: 3x = 12

Step 4: Divide by 3: x = 4

Check: 5(4) - 3 = 17, and 2(4) + 9 = 17 ✓

Example 3: With Parentheses

Problem: Solve 2(x + 4) = 14

Step 1: Distribute: 2x + 8 = 14

Step 2: Subtract 8: 2x = 6

Step 3: Divide by 2: x = 3

Check: 2(3 + 4) = 2(7) = 14 ✓

✏️ Practice Problems

Work through each problem. Try to solve it yourself before revealing the solution.

Problem 1: Solve 4x - 5 = 19

Show Solution

4x - 5 = 19

4x = 24 (add 5 to both sides)

x = 6 (divide by 4)

Problem 2: Solve 7 + 2x = 21

Show Solution

7 + 2x = 21

2x = 14 (subtract 7)

x = 7 (divide by 2)

Problem 3: Solve 6x - 4 = 3x + 11

Show Solution

6x - 4 = 3x + 11

3x - 4 = 11 (subtract 3x)

3x = 15 (add 4)

x = 5 (divide by 3)

Problem 4: Solve 3(x - 2) = 15

Show Solution

3(x - 2) = 15

3x - 6 = 15 (distribute)

3x = 21 (add 6)

x = 7 (divide by 3)

Problem 5: Solve 5x + 8 = 2x + 23

Show Solution

5x + 8 = 2x + 23

3x + 8 = 23 (subtract 2x)

3x = 15 (subtract 8)

x = 5 (divide by 3)

Problem 6: Solve -2x + 10 = 4

Show Solution

-2x + 10 = 4

-2x = -6 (subtract 10)

x = 3 (divide by -2)

Problem 7: Solve 4(x + 1) = 2(x + 5)

Show Solution

4(x + 1) = 2(x + 5)

4x + 4 = 2x + 10 (distribute both sides)

2x + 4 = 10 (subtract 2x)

2x = 6 (subtract 4)

x = 3 (divide by 2)

Problem 8: Solve x/3 + 5 = 9

Show Solution

x/3 + 5 = 9

x/3 = 4 (subtract 5)

x = 12 (multiply by 3)

Problem 9: Solve 8 - 3x = 2

Show Solution

8 - 3x = 2

-3x = -6 (subtract 8)

x = 2 (divide by -3)

Problem 10: Solve 2(3x - 1) = 4x + 6

Show Solution

2(3x - 1) = 4x + 6

6x - 2 = 4x + 6 (distribute)

2x - 2 = 6 (subtract 4x)

2x = 8 (add 2)

x = 4 (divide by 2)

✅ Check Your Understanding

Answer these questions to assess your understanding of solving linear equations.

  1. When solving 5x + 3 = 18, what is the first step you should take?
  2. If you get x = 4 as your answer, how can you verify it is correct?
  3. When you have variables on both sides, what strategy do you use?
  4. Why is it important to perform the same operation on both sides of an equation?

🚀 Next Steps

  • If you scored 8/10 or better, move on to Word Problems
  • If you struggled with variables on both sides, review Lesson 2
  • Practice checking your answers by substitution
  • Try timing yourself to build speed and accuracy