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Exercises Equations and inequalities

Example 5 from Algebra and Trigonometry, 2.7 Linear Inequalities and Absolute Value Inequalities

Solving an Inequality Algebraically

Solve the inequality: $13 - 7 x \geq 10 x - 4.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Solving this inequality is similar to solving an equation up until the last step.

$\begin{array}{l} 13 - 7 x \geq 10 x - 4 \\ 13 - 17 x \geq −4 & Move variable terms to one side of the inequality . \\ −17 x \geq −17 & Isolate the variable term . \\ x \leq 1 & Dividing both sides by −17 reverses the inequality . \end{array}$
The solution set is given by the interval $(- \infty, 1],$ or all real numbers less than and including 1.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the inequality and write the answer using interval notation: $- x + 4 < \frac{1}{2} x + 1.$

How did it go?

PreviousDemonstrating the Multiplication Property Next Solving an Inequality with Fractions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.