Equations & Inequalities
Solve linear equations and inequalities
Solving Linear Equations
An equation has an equals sign (=). To solve, isolate the variable by performing the same operation on both sides. What you do to one side, you must do to the other.
Example
Solving Equations Step by Step
3x + 7 = 22
3x = 22 − 7
3x = 15
x = 5
2(x − 3) = 10
2x − 6 = 10
2x = 16
x = 8
Inequalities
An inequality uses <, >, ≤ or ≥ instead of =. Solve the same way as equations, BUT if you multiply or divide by a negative number, flip the inequality sign.
Example
Solving Inequalities
2x + 3 < 11
2x < 8
x < 4
−3x ≥ 12
x ≤ −4 (flip sign because we divided by −3)
Note
Remember
Equations: balanced scales — keep both sides equal. Inequalities: remember to flip the sign when multiplying or dividing by a negative. Represent solutions on a number line.
Key Vocabulary
EquationA mathematical statement that two expressions are equal
InequalityA statement that one expression is greater or less than another
SolutionThe value that makes the equation true
IsolateGet the variable alone on one side
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