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Inequalities

Solve one-step linear inequalities

Solving a linear inequality in one variable is much like solving a linear equation in one variable. To solve the inequality, you isolate the variable on one side using transformations that produce equivalent inequalities, which have the same solution(s).

Solve x+5≥3. Graph the solution.

 x+5 ≥ 3 Write original inequality x+5-5 ≥ 3-5 Subtract 5 from each side x ≥ -2 Simplify

The solution is all real numbers greater than or equal to -2.

Solve $\frac{a}{3}\;\leq\;12$. Graph the solution.

 $\frac{a}{3}\;\leq\;12$ Write original inequality. $3\;\cdot\;\frac{a}{3}\;\leq\;3\;\cdot\;12$ Multiply each side by positive 3. $a\;\leq\;36$ Simplify.

The solution is all real numbers less than or equal to 36.