91Ó°ÊÓ

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{2 x-5}{-4}>5\)

Solve each equation for \(y\). $$x-2 y=-6$$

Complete the six problem-solving steps to solve each problem. In 2015 , the corporations securing the most U.S. patents were IBM and Samsung. Together, the two corporations secured a total of 12,368 patents, with Samsung receiving 2250 fewer patents than IBM. How many patents did each corporation secure? (Data from U.S. Patent and Trademark Office.) Step 1 Read the problem carefully. We are asked to find ______ . 2 Assign a variable. Let \(x=\) the number of patents that IBM secured. Step Then \(x-2250=\) the number of ______ . Step 3 Write an equation. ____\(+ _____ \ldots=12,368\) Step 4 Solve the equation. \(x=\) ______ . \(\begin{array}{llll}\text { Step } 5 & \text { State the answer. } & \text { IBM secured } & \text { patents. Samsung secured } & \text { patents. }\end{array}\) Step 6 Check. The number of Samsung patents was _____ fewer than the number of _____ The total number of patents was \(7309+\) _____ \(= ______\).

Solve each equation for \(y\). $$x-5 y=-20$$

On an automobile trip, Laura maintained a steady rate for the first two hours. Rush-hour traffic slowed her rate by 25 mph for the last part of the trip. The entire trip, a distance of \(125 \mathrm{mi},\) took \(2 \frac{1}{2} \mathrm{hr} .\) What was her rate during the first part of the trip?

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{3 x-2}{-5}<6\)

Solve each equation. $$ |0.04 x-3|=5.96 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(2(3-2 x)=x-4\)

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x|>3 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ 3 x-4 \leq 8 \text { and }-4 x+1 \geq-15 $$