91Ó°ÊÓ

graph the given inequalities on the number line. \((x \leq 5 \text { or } x \geq 8)\) and \((3 < x < 10)\)

Solve the given problems by setting up and solving appropriate inequalities. Graph each solution. For \(-6

Solve the given problems by setting up and solving appropriate inequalities. Graph each solution. For \(8>-x>-4,\) find \(a\) and \(b\) such that \(a

Use a calculator to display the solution of the given inequality or system of inequalities. $$\begin{aligned} &y \geq\left|4-x^{2}\right|\\\ &y<2 \ln |x| \end{aligned}$$

Solve the given inequalities graphically by using a calculator. See Example 10. $$4 \cos 2 x>2 x-3$$

Use inequalities involving absolute values to solve the given problems. The Mach number \(M\) of a moving object is the ratio of its velocity \(v\) to the velocity of sound \(v_{s},\) and \(v_{s}\) varies with temperature. A jet traveling at \(1650 \mathrm{km} / \mathrm{h}\) changes its altitude from \(500 \mathrm{m}\) to \(5500 \mathrm{m}\) At \(\left.500 \mathrm{m} \text { (with the temperature at } 27^{\circ} \mathrm{C}\right), v_{s}=1250 \mathrm{km} / \mathrm{h},\) and at \(5500 \mathrm{m}\left(-3^{\circ} \mathrm{C}\right), v_{s}=1180 \mathrm{km} / \mathrm{h} .\) Express the range of \(M,\) using an inequality with absolute values.

graph the given inequalities on the number line. \((x < 7 \text { and } x > 2)\) or \((x \geq 10 \text { or } x < 1)\)

Use inequalities involving absolute values to solve the given problems. The diameter \(d\) of a certain type of tubing is \(3.675 \mathrm{cm}\) with a tolerance of \(0.002 \mathrm{cm} .\) Express this as an inequality with absolute values.

answer the given questions about the inequality \(0 < a < b\) Is \(a^{2}

Use inequalities to solve the given problems. Is \(x^{2}>x\) for all \(x ?\) Explain.