Equations
Solve simple linear equations
What is an Equation?
An equation is a mathematical statement that two things are equal. It has an equals sign (=) in the middle. For example: 2x + 3 = 11. Solving an equation means finding the value of the variable that makes the statement true.
Solving One-Step Equations
Use inverse (opposite) operations to isolate the variable.
x + 5 = 12 → subtract 5 from both sides → x = 7
x − 3 = 10 → add 3 to both sides → x = 13
3x = 18 → divide both sides by 3 → x = 6
x/4 = 5 → multiply both sides by 4 → x = 20
Example
Solving Two-Step Equations
Solve: 2x + 3 = 11
Step 1: Subtract 3 from both sides → 2x = 8
Step 2: Divide both sides by 2 → x = 4
Check: 2(4) + 3 = 8 + 3 = 11 ✓
Solve: 5x − 7 = 18
Step 1: Add 7 → 5x = 25
Step 2: Divide by 5 → x = 5
Check: 5(5) − 7 = 25 − 7 = 18 ✓
Note
Remember
Whatever you do to one side of the equation, you MUST do to the other side. Always check your answer by substituting it back into the original equation.
Key Vocabulary
EquationA statement that two expressions are equal
SolveTo find the value of the unknown variable
InverseThe opposite operation (+ and − are inverses)
IsolateTo get the variable alone on one side
SolutionThe value that makes the equation true
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