Chapter 1

Dimensions of a Lot A square plot of land has a building 60 \(\mathrm{ft}\) long and 40 \(\mathrm{ft}\) wide at one comer. The rest of the land outside the building forms a parking lot. If the parking lot has area \(12,000 \mathrm{ft}^{2},\) what are the dimensions of the entire plot of land?

Evaluate the expression and write the result in the form a bi. $$ \frac{5-i}{3+4 i} $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x(2-3 x) \leq 0 $$

Find all real solutions of the equation. $$ 8 x^{2}-6 x-9=0 $$

\(5-60\) Find all real solutions of the equation. $$ \left(\frac{x}{x+2}\right)^{2}=\frac{4 x}{x+2}-4 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{6}{x-3}=\frac{5}{x+4}\)

Dimensions of a Lot A half-acre building lot is five times as long as it is wide. What are its dimensions? [Note: 1 acre \(=43,560 \mathrm{ft}^{2}\) .

Evaluate the expression and write the result in the form a bi. $$ \frac{26+39 i}{2-3 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 4|x+2|-3<13 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}-3 x-18 \leq 0 $$

Find all real solutions of the equation. $$ 3 x^{2}+6 x-5=0 $$

\(5-60\) Find all real solutions of the equation. $$ x^{4}-13 x^{2}+40=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{3}{x+1}-\frac{1}{2}=\frac{1}{3 x+3}\)

Evaluate the expression and write the result in the form a bi. $$ \frac{25}{4-3 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 3-|2 x+4| \leq 1 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}+5 x+6>0 $$

Find all real solutions of the equation. $$ x^{2}-6 x+1=0 $$

\(5-60\) Find all real solutions of the equation. $$ x^{4}-5 x^{2}+4=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{4}{x-1}+\frac{2}{x+1}=\frac{35}{x^{2}-1}\)

Evaluate the expression and write the result in the form a bi. $$ \frac{10 i}{1-2 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 8-|2 x-1| \geq 6 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x^{2}+x \geq 1 $$

Find all real solutions of the equation. $$ z^{2}-\frac{3}{2} z+\frac{9}{16}=0 $$

\(5-60\) Find all real solutions of the equation. $$ 2 x^{4}+4 x^{2}+1=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{2 x-7}{2 x+4}=\frac{2}{3}\)

Framing a Painting Ali paints with watercolors on a sheet of paper 20 in. wide by 15 in. high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 in. How wide is the strip of the mat showing around the picture?

Evaluate the expression and write the result in the form a bi. $$ (2-3 i)^{-1} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 7|x+2|+5>4 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}

Find all real solutions of the equation. $$ 2 y^{2}-y-\frac{1}{2}=0 $$

\(5-60\) Find all real solutions of the equation. $$ x^{6}-2 x^{3}-3=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{12 x-5}{6 x+3}=2-\frac{5}{x}\)

Dimensions of a Poster \(\quad\) A poster has a rectangular printed area 100 \(\mathrm{cm}\) by 140 \(\mathrm{cm}\) and a blank strip of uniform width around the edges. The perimeter of the poster is 1\(\frac{1}{2}\) times the perimeter of the printed area. What is the width of the blank strip?

Evaluate the expression and write the result in the form a bi. $$ \frac{4+6 i}{3 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ \frac{1}{2}\left|4 x+\frac{1}{3}\right|>\frac{5}{6} $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ 3 x^{2}-3 x<2 x^{2}+4 $$

Find all real solutions of the equation. $$ 4 x^{2}+16 x-9=0 $$

\(5-60\) Find all real solutions of the equation. $$ x^{6}-26 x^{3}-27=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{1}{z}-\frac{1}{2 z}-\frac{1}{5 z}=\frac{10}{z+1}\)

Evaluate the expression and write the result in the form a bi. $$ \frac{-3+5 i}{15 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 2\left|\frac{1}{2} x+3\right|+3 \leq 51 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ 5 x^{2}+3 x \geq 3 x^{2}+2 $$

Find all real solutions of the equation. $$ 0=x^{2}-4 x+1 $$

\(5-60\) Find all real solutions of the equation. $$ x^{8}+15 x^{4}=16 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{1}{1-\frac{3}{2+w}}=60\)

Evaluate the expression and write the result in the form a bi. $$ \frac{1}{1+i}-\frac{1}{1-i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ 1 \leq|x| \leq 4 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}>3(x+6) $$

Find all real solutions of the equation. $$ w^{2}=3(w-1) $$

\(5-60\) Find all real solutions of the equation. $$ x^{4 / 3}-5 x^{2 / 3}+6=0 $$