Example

Example: Solving and Graphing 15<35z-15 < \frac{3}{5}z

The linear inequality 15<35z-15 < \frac{3}{5}z is solved using the Multiplication Property of Inequality. First, isolate the variable by multiplying both sides by the reciprocal of the coefficient, which is 53\frac{5}{3}. Because 53\frac{5}{3} is a positive number, the inequality sign is unchanged, returning the true statement 25<z-25 < z. To make graphing more intuitive, this can be rewritten with the variable on the left as z>25z > -25. The solution is then graphed on a number line with a left parenthesis at 25-25 and shaded to the right. In interval notation, this represents the interval (25,)(-25, \infty).

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Updated 2026-04-22

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Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax

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