Linear Equations Practice

Practice solving equations where the variable has a power of one. Linear equations are one of the most important foundations for algebra, graphing, formulas, and college-level math.

Skill 1: Solving One-Step Equations

A one-step equation can be solved using one opposite operation. If a number is added to the variable, subtract it from both sides. If a number is subtracted, add it to both sides.

Worked Example

Problem: Solve x + 9 = 15

Step 1: The variable x has 9 added to it.

Step 2: Use the opposite operation. Subtract 9 from both sides.

x + 9 - 9 = 15 - 9

Step 3: Simplify.

x = 6

Answer: x = 6

Try These

  1. x + 4 = 10
  2. x - 6 = 8
  3. x + 12 = 20
  4. x - 3 = 11
  5. x + 7 = 18

Answer Key

  1. x = 6
  2. x = 14
  3. x = 8
  4. x = 14
  5. x = 11

Mastery Check

You are ready to move on when you can identify the operation attached to the variable and use the opposite operation to isolate it.

Skill 2: Solving Two-Step Equations

A two-step equation needs two opposite operations to isolate the variable. Usually, you undo addition or subtraction first, then undo multiplication or division. The goal is to get the variable by itself.

Worked Example

Problem: Solve 3x - 4 = 8

Step 1: The variable term is 3x. First, undo the -4 by adding 4 to both sides.

3x - 4 + 4 = 8 + 4

3x = 12

Step 2: Now undo multiplication by 3. Divide both sides by 3.

3x ÷ 3 = 12 ÷ 3

x = 4

Answer: x = 4

Try These

  1. 2x + 3 = 11
  2. 4x - 5 = 15
  3. 3x + 6 = 18
  4. 5x - 2 = 23
  5. 6x + 4 = 40

Answer Key

  1. x = 4
  2. x = 5
  3. x = 4
  4. x = 5
  5. x = 6

Mastery Check

You are ready to move on when you can solve an equation by undoing addition or subtraction first, then undoing multiplication or division.

Skill 3: Equations with Variables on Both Sides

Some equations have variables on both sides of the equal sign. To solve them, move the variable terms to one side and the number terms to the other side. Then use opposite operations to isolate the variable.

Worked Example

Problem: Solve 5x + 2 = 2x + 14

Step 1: Move the smaller variable term to the other side.

Subtract 2x from both sides.

5x - 2x + 2 = 2x - 2x + 14

3x + 2 = 14

Step 2: Move the number away from the variable.

Subtract 2 from both sides.

3x + 2 - 2 = 14 - 2

3x = 12

Step 3: Divide both sides by 3.

x = 4

Answer: x = 4

Try These

  1. 4x + 3 = x + 12
  2. 6x - 5 = 2x + 7
  3. 8x + 1 = 3x + 16
  4. 7x - 4 = 4x + 8
  5. 9x + 2 = 5x + 18

Answer Key

  1. x = 3
  2. x = 3
  3. x = 3
  4. x = 4
  5. x = 4

Mastery Check

You are ready to move on when you can collect variable terms on one side, collect number terms on the other side, and then solve.

Skill 4: Distributive Property Equations

Some equations include parentheses. Use the distributive property first, then solve the equation. The distributive property means multiplying the outside number by each term inside the parentheses.

Worked Example

Problem: Solve 3(x + 2) = 18

Step 1: Distribute the 3 to each term inside the parentheses.

3(x + 2) = 3x + 6

So the equation becomes:

3x + 6 = 18

Step 2: Subtract 6 from both sides.

3x + 6 - 6 = 18 - 6

3x = 12

Step 3: Divide both sides by 3.

x = 4

Answer: x = 4

Try These

  1. 2(x + 3) = 14
  2. 4(x - 2) = 20
  3. 3(x + 5) = 24
  4. 5(x - 1) = 30
  5. 6(x + 2) = 48

Answer Key

  1. x = 4
  2. x = 7
  3. x = 3
  4. x = 7
  5. x = 6

Mastery Check

You are ready to move on when you can distribute first, simplify the equation, and then isolate the variable.

Skill 5: Checking Your Solution

Checking your solution means substituting your answer back into the original equation. If both sides become equal, your answer is correct. This is one of the best habits students can build in algebra.

Worked Example

Problem: Check whether x = 4 is the solution to 3x - 4 = 8.

Step 1: Start with the original equation.

3x - 4 = 8

Step 2: Substitute x = 4.

3(4) - 4 = 8

Step 3: Simplify the left side.

12 - 4 = 8

8 = 8

Answer: Yes, x = 4 is correct because both sides are equal.

Try These

  1. Check whether x = 6 is the solution to x + 4 = 10.
  2. Check whether x = 5 is the solution to 2x + 3 = 11.
  3. Check whether x = 3 is the solution to 4x + 3 = 15.
  4. Check whether x = 7 is the solution to 3(x + 2) = 27.
  5. Check whether x = 4 is the solution to 5x + 2 = 22.

Answer Key

  1. Yes. 6 + 4 = 10, so 10 = 10.
  2. No. 2(5) + 3 = 13, not 11.
  3. Yes. 4(3) + 3 = 15, so 15 = 15.
  4. Yes. 3(7 + 2) = 27, so 27 = 27.
  5. Yes. 5(4) + 2 = 22, so 22 = 22.

Note: Problem 4 is a reminder that checking means substituting the value into the original equation. If both sides are equal, the solution is correct.

Mastery Check

You are ready to move on when you can substitute your answer into the original equation and decide whether the left side equals the right side.

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