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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 \(x\). \[2(3-x)+4x-1=4-2(x+1)-3 \]

Let's see these steps in action.

Step 1: Expand the brackets.

\[6-2x+4x=4-2x-2-3\]

Step 2: Gather terms:.

\[-2x+4x+2x=4-2-3-6\]

Step 3: Combine like terms.

\[4x = -7\]

Step 4: Divide across to isolate the variable.

\[x = {-7 \over 4}\]

 

Example 2: Solve the equation below for \(x\). \[8-\frac{7x }{4}=15 \]

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

\[4(8-\frac{7x }{4})=4\times15 \]

Step 2: Remove brackets

\[4\times8 - 4(\frac{7x }{4})=4\times15 \]

Step 3: Simplify

\[32 - 7x = 60\]

Step 4: Collect like terms

\[-7x=60-32\]

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 \(x\). \[3(x-m)=12-x\]

Step 1: Remove brackets

\[3x-3m=12-x \]

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 \(x\)

\[x=3+ \frac{3m}{4} \]

Example 4: Solve the equation below for \(x\). \[\frac{5(x-1)}{6} - \frac{3x+11}{8}=1\]

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

\[48\times\frac{5(x-1)}{6} - 48\times\frac{3x+11}{8}=1\times48\]

Step 2: Simplify

\[8\times5(x-1) - 6(3x+11)=48 \]

Step 3: Expand the brackets

\[40x-40 - 18x-66=48 \]

Step 4: Collect like terms

\[40x-18x=48+40+66\]

Step 5: Combine like terms

\[22x=154 \]

Step 6: Divide both sides by the coefficient of \(x\)

\[x=7 \]

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