Chapter 1

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \sqrt{3} x+\sqrt{12}=\frac{x+5}{\sqrt{3}} $$

Solve the inequality. Express the answer using interval notation. $$ |5 x-2|<6 $$

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 \(=43,560 \mathrm{ft}^{2} . ]\)

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -3 \leq 3 x+7 \leq \frac{1}{2} $$

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

1–54 ? Find all real solutions of the equation. $$ x^{6}-2 x^{3}-3=0 $$

Find all real solutions of the equation. \(3 x^{2}+7 x+4=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2}{3} x-\frac{1}{4}=\frac{1}{6} x-\frac{1}{9} $$

Solve the inequality. Express the answer using interval notation. $$ \left|\frac{x-2}{3}\right|<2 $$

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{2}{3} \geq \frac{2 x-3}{12}>\frac{1}{6} $$

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

1–54 ? Find all real solutions of the equation. $$ x^{6}-26 x^{3}-27=0 $$

Find all real solutions of the equation. \(x^{2}+3 x+1=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2}{x}-5=\frac{6}{x}+4 $$

Solve the inequality. Express the answer using interval notation. $$ \left|\frac{x+1}{2}\right| \geq 4 $$

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -\frac{1}{2} \leq \frac{4-3 x}{5} \leq \frac{1}{4} $$

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

1–54 ? Find all real solutions of the equation. $$ x^{8}+15 x^{4}=16 $$

Find all real solutions of the equation. \(2 x^{2}-8 x+4=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{6}{x-3}=\frac{5}{x+4} $$

Solve the inequality. Express the answer using interval notation. $$ |x+6|<0.001 $$

\(33-66\) me solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ (x+2)(x-3)<0 $$

Framing a Painting \(\quad\) Al 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 \(a+b i .\) $$ \frac{10 i}{1-2 i} $$

1–54 ? Find all real solutions of the equation. $$ x^{4 / 3}-5 x^{2 / 3}+6=0 $$

Find all real solutions of the equation. \(x^{2}+12 x-27=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{3}{x+1}-\frac{1}{2}=\frac{1}{3 x+3} $$

Solve the inequality. Express the answer using interval notation. $$ |x-a|

\(33-66\) me solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ (x-5)(x+4) \geq 0 $$

Mixture Problem What quantity of a 60\(\%\) acid solution must be mixed with a 30\(\%\) solution to produce 300 \(\mathrm{mL}\) of a 50\(\%\) solution?

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

1–54 ? Find all real solutions of the equation. $$ \sqrt{x}-3 \sqrt[4]{x}-4=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{4}{x-1}+\frac{2}{x+1}=\frac{35}{x^{2}-1} $$

Solve the inequality. Express the answer using interval notation. $$ 4|x+2|-3<13 $$

\(33-66\) me solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x(2 x+7) \geq 0 $$

Mixture Problem A jeweler has five rings, each weighing \(18 \mathrm{g},\) made of an alloy of 10\(\%\) silver and 90\(\%\) gold. He decides to melt down the rings and add enough silver to reduce the gold content to 75\(\% .\) How much silver should he add?

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

1–54 ? Find all real solutions of the equation. $$ 4(x+1)^{1 / 2}-5(x+1)^{3 / 2}+(x+1)^{5 / 2}=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2 x-7}{2 x+4}=\frac{2}{3} $$

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

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x(2-3 x) \leq 0 $$

Mixture Problem \(\quad\) A pot contains 6 \(\mathrm{L}\) of brine at a con- centration of 120 \(\mathrm{g} / \mathrm{L}\) . How much of the water should be boiled off to increase the concentration to 200 \(\mathrm{g} / \mathrm{L} ?\)

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

1–54 ? Find all real solutions of the equation. $$ 2(x-4)^{7 / 3}-(x-4)^{4 / 3}-(x-4)^{1 / 3}=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{12 x-5}{6 x+3}=2-\frac{5}{x} $$

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

\(33-66\) . Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x^{2}-3 x-18 \leq 0 $$