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.

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- Basic Laws
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The following steps will help you solve linear equations.

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

`Example 1`

Solve the equation below for \(x\). \[2(3-x)+4x-1=4-2(x+1)-3 \]

`Solution`

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 \(x\). \[8-\frac{7x }{4}=15 \]

`Solution`

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 \(x\). \[3(x-m)=12-x\]

`Solution`

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

`Solution`

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 \(x\)

\[x=7 \]

- Last Updated: Mar 18, 2024 3:47 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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