Year 7: Solve Linear Equations

Solving Linear Equations - Key Principles

• Isolate the Variable: Your goal is to get the variable by itself on one side of the equals sign
• Use Inverse Operations: Do the opposite operation to move terms (add/subtract, multiply/divide)
• Keep It Balanced: Whatever you do to one side, you MUST do to the other side

Steps to Solve Linear Equations

1. Simplify if needed: Expand brackets or combine like terms on each side
2. Move constants: Add or subtract to move numbers away from the variable term
3. Isolate the variable: Multiply or divide to get the variable by itself
4. Check your answer: Substitute your solution back into the original equation

Examples

Example 1:$2x+3=7$

1. Subtract 3 from both sides: $2x=4$
2. Divide both sides by 2: $x=2$
3. Check: $2\left(2\right)+3=4+3=7$ ✓

Example 2:$x/3-1=2$

1. Add 1 to both sides: $x/3=3$
2. Multiply both sides by 3: $x=9$
3. Check: $9/3-1=3-1=2$ ✓

Example 3:$3(x-2)=12$

1. Expand: $3x-6=12$
2. Add 6 to both sides: $3x=18$
3. Divide by 3: $x=6$
4. Check: $3(6-2)=3\left(4\right)=12$ ✓

Example 4:$5x-2=3x+8$

1. Subtract 3x from both sides: $2x-2=8$
2. Add 2 to both sides: $2x=10$
3. Divide by 2: $x=5$
4. Check: $5\left(5\right)-2=25-2=23$, and $3\left(5\right)+8=15+8=23$ ✓