Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.5 Inequalities - R.5 Exercises - Page R-21: 26


$(-\infty$, $\frac{50}{9})$

Work Step by Step

$\frac{8}{3}(z-4)$$\leq$$\frac{2}{9}(3z+2)$ 1. Multiply through $\frac{8}{3}z$-$\frac{32}{3}$$\leq$$\frac{2}{3}z$+$\frac{4}{9}$ 2. Subtract/add from each side to get any polynomials with a variable on one side and any without a variable on the other $\frac{6}{3}z$$\leq$$\frac{100}{9}$ 3. Simplify any possible fractions 2z$\leq$$\frac{100}{9}$ 4. Multiply by $\frac{1}{2}$ on both sides to get the variable by itself z$\leq$$\frac{50}{9}$ 5. Plug $\frac{50}{9}$ back into the original problem for z to get $\frac{112}{27}$ 6. Test any number between $\frac{112}{27}$ and z$\leq$$\frac{50}{9}$ into the original equation 7. Since any number you test will be negative, your interval starts at $-\infty$ and ends with the interval found earlier: $\frac{50}{9}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.