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Exercises Equations and inequalities

Example 4 from Algebra and Trigonometry, 2.7 Linear Inequalities and Absolute Value Inequalities

Demonstrating the Multiplication Property

Illustrate the multiplication property for inequalities by solving each of the following:

ⓐ $3 x < 6$
ⓑ $−2 x - 1 \geq 5$
ⓒ $5 - x > 10$

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.

1
Solution
1. ⓐ
  $\begin{array}{l} 3 x < 6 \\ \frac{1}{3} (3 x) < (6) \frac{1}{3} \\ x < 2 \end{array}$
2. ⓑ
  $\begin{array}{l} - 2 x - 1 \geq 5 \\ - 2 x \geq 6 \\ (- \frac{1}{2}) (- 2 x) \geq (6) (- \frac{1}{2}) & Multiply by - \frac{1}{2} . \\ x \leq - 3 & Reverse the inequality . \end{array}$
3. ⓒ
  $\begin{array}{l} 5 - x > 10 \\ - x > 5 \\ (- 1) (- x) > (5) (- 1) & Multiply by - 1. \\ x < - 5 & Reverse the inequality . \end{array}$

Your turn

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

Solve: $4 x + 7 \geq 2 x - 3.$

How did it go?

PreviousDemonstrating the Addition Property Next Solving an Inequality Algebraically

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.