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Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

Steps to Solve Linear Equations

The following steps will help you solve linear equations.

  1. Expand any brackets in the equation
  2. Gather terms with variables to left side of the equal sign, and numbers to right side of the equal sign.
  3. Combine the like terms
  4. Divide across to isolate the variable.

Examples

Example 1

Solve the equation below for x. 2(3x)+4x1=42(x+1)3

Solution

Let's see these steps in action.

Step 1: Expand the brackets.

62x+4x=42x23

Step 2: Gather terms:.

2x+4x+2x=4236

Step 3: Combine like terms.

4x=7

Step 4: Divide across to isolate the variable.

x=74

 

Example 2

Solve the equation below for x. 87x4=15

Solution

Step 1: Multiply both sides of the equation by the LCM, 4

4(87x4)=4×15

Step 2: Remove brackets

4×84(7x4)=4×15

Step 3: Simplify

327x=60

Step 4: Collect like terms

7x=6032

Step 5: Combine like terms

7x=28

Step 6: Divide both sides by the coefficient of x

x=4

Example 3

Solve the equation below for x. 3(xm)=12x

Solution

Step 1: Remove brackets

3x3m=12x

Step 2: Collect like terms

3x+x=12+3m

Step 3: Combine like terms

4x=12+3m

Step 4: Divide both sides by the coefficient of x

x=3+3m4

Example 4

Solve the equation below for x. 5(x1)63x+118=1

Solution

Step 1: Multiply both sides of the equation by the LCM, 48

48×5(x1)648×3x+118=1×48

Step 2: Simplify

8×5(x1)6(3x+11)=48

Step 3: Expand the brackets

40x4018x66=48

Step 4: Collect like terms

40x18x=48+40+66

Step 5: Combine like terms

22x=154

Step 6: Divide both sides by the coefficient of x

x=7