91Ó°ÊÓ

Solve each formula for the specified variable. \(y=m x+b\) (slope-intercept form of a linear equation) (a) for \(x\) (b) for \(m\)

Solve each equation. $$ |0.3 x|=9 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ 5(x+3)-8(2 x-6)=12 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-2.5 x \leq-1.25\)

Johnny leaves Memphis to visit his cousin Anne, who lives in the town of Hornsby, Tennessee, 80 mi away. He travels at an average rate of 50 mph. One- half hour later, Anne leaves to visit Johnny, traveling at an average rate of \(60 \mathrm{mph}\). How long after Anne leaves will it be before they meet?

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 \(7309+\) _____ \(= ______\).

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 problem. The John Hancock Center in Chicago has a rectangular base. The length of the base measures \(65 \mathrm{ft}\) less than twice the width. The perimeter of the base is \(860 \mathrm{ft}\). What are the dimensions of the base?

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

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x|>5 $$