Chapter 1

Solve each equation by the zero-factor property. $$-4 x^{2}+x=-3$$

Solve each problem. Concept Check Which one or more of the following cannot be a correct equation to solve a geometry problem, if \(x\) represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) A. \(2 x+2(x-1)=14\) B. \(-2 x+7(5-x)=52\) C. \(5(x+2)+5 x=10\) D. \(2 x+2(x-3)=22\)

Solve each equation. $$\left|\frac{2 x+3}{3 x-4}\right|=1$$

Write each number as the product of a real number and i. $$\sqrt{-36}$$

The length of each side of a square is 5 in. more than the length of each side of a smaller square. The difference of the areas of the squares is 95 in. \(^{2} .\) Find the lengths of the sides of the two squares.

Solve each equation. $$\frac{-x}{x+1}-\frac{1}{x-1}=\frac{-2}{x^{2}-1}$$

Solve each inequality. Write each solution set in interval notation. $$6 x-(2 x+3) \geq 4 x-5$$

Solve each equation. $$4[2 x-(3-x)+5]=-6 x-28$$

Solve each equation by the zero-factor property. $$-6 x^{2}+7 x=-10$$

Solve each problem. Margaret drove to a business appointment at 50 mph. Her average speed on the return trip was \(40 \mathrm{mph}\). The return trip took \(\frac{1}{4} \mathrm{hr}\) longer because of heavy traffic. How far did she travel to the appointment?

Solve each equation. $$|2 x-3|=|5 x+4|$$

Write each number as the product of a real number and i. $$\sqrt{-10}$$

Solve each equation. $$\frac{5}{x^{2}}-\frac{43}{x}=18$$

Solve each inequality. Write each solution set in interval notation. $$8 x-3 x+2<2(x+7)$$

Solve each equation. $$\frac{1}{14}(3 x-2)=\frac{x+10}{10}$$

Solve each equation by the zero-factor property. $$x^{2}-100=0$$

Solve each problem. Distance between Cities On a vacation, Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities if his total traveling time was 32 hr?

Solve each equation. $$|x+1|=|1-3 x|$$

Write each number as the product of a real number and i. $$\sqrt{-15}$$

Solve each equation. $$\frac{7}{x^{2}}+\frac{19}{x}=6$$

Solve each inequality. Write each solution set in interval notation. $$2-4 x+5(x-1)<-6(x-2)$$

Solve each equation. $$\frac{1}{15}(2 x+5)=\frac{x+2}{9}$$

Solve each equation by the zero-factor property. $$x^{2}-64=0$$

Solve each equation. $$|4-3 x|=|2-3 x|$$

Write each number as the product of a real number and i. $$\sqrt{-288}$$

Solve each inequality. Write each solution set in interval notation. $$\frac{4 x+7}{-3} \leq 2 x+5$$

Solve each equation. $$2=\frac{3}{2 x-1}+\frac{-1}{(2 x-1)^{2}}$$

Solve each equation. $$0.2 x-0.5=0.1 x+7$$

Solve each equation by the zero-factor property. $$4 x^{2}-4 x+1=0$$

Solve each problem. Speed of a Plane Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In \(\frac{1}{2}\) hr, the planes are 275 mi apart. What are their speeds?

Solve each equation. $$|3-2 x|=|5-2 x|$$

Write each number as the product of a real number and i. $$\sqrt{-500}$$

A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover \(24 \mathrm{ft}^{2}\) for the border, how wide can the border be?

Solve each inequality. Write each solution set in interval notation. $$\frac{2 x-5}{-8} \leq 1-x$$

Solve each equation. $$6=\frac{7}{2 x-3}+\frac{3}{(2 x-3)^{2}}$$

Solve each equation. $$0.01 x+3.1=2.03 x-2.96$$

Solve each equation by the zero-factor property. $$9 x^{2}-12 x+4=0$$

Solve each problem. Running Times Mary and Janet are running in the Apple Hill Fun Run. Mary runs at 7 mph, Janet at \(5 \mathrm{mph}\). If they start at the same time, how long will it be before they are \(1.5 \mathrm{mi}\) apart?

Solve each equation. $$|5 x-2|=|2-5 x|$$

Write each number as the product of a real number and i. $$-\sqrt{-18}$$

A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 832 in. \(^{3}\), what were the original dimensions of the piece of metal?

Solve each inequality. Write each solution set in interval notation. $$\frac{1}{3} x+\frac{2}{5} x-\frac{1}{2}(x+3) \leq \frac{1}{10}$$

Solve each equation. $$\frac{2 x-5}{x}=\frac{x-2}{3}$$

Solve each equation. $$-4(2 x-6)+8 x=5 x+24+x$$

Solve each equation by the zero-factor property. $$25 x^{2}+30 x+9=0$$

Write each number as the product of a real number and i. $$-\sqrt{-80}$$

Solve each inequality. Write each solution set in interval notation. $$-\frac{2}{3} x-\frac{1}{6} x+\frac{2}{3}(x+1) \leq \frac{4}{3}$$

Solve each equation. $$\frac{x+4}{2 x}=\frac{x-1}{3}$$

Solve each equation. $$-8(3 x+4)+6 x=4(x-8)+4 x$$

Solve each equation by the zero-factor property. $$36 x^{2}+60 x+25=0$$