Chapter 1

Solve the equation. $$ |4 x|=24 $$

Express the given quantity in terms of the indicated variable. The sum of three consecutive integers; \(\quad n=\) first integer of the three

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ x-3>0 $$

Find the real and imaginary parts of the complex number. $$ 5-7 i $$

1–54 ? Find all real solutions of the equation. $$ x^{3}=16 x $$

Solve the equation by factoring. \(x^{2}+x-12=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{4 x+7=9 x-3} \\ {\text { (a) } x=-2} & {\text { (b) } x=2}\end{array} $$

Solve the equation. $$ |6 x|=15 $$

Express the given quantity in terms of the indicated variable. The sum of three consecutive integers; \(\quad n=\) middle integer of the three

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ x+1<2 $$

Find the real and imaginary parts of the complex number. $$ -6+4 i $$

1–54 ? Find all real solutions of the equation. $$ x^{5}=27 x^{2} $$

Solve the equation by factoring. \(x^{2}+3 x-4=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{2-5 x=8+x} \\ {\text { (a) } x=-1} & {\text { (b) } x=1}\end{array} $$

Solve the equation. $$ 5|x|+3=28 $$

Express the given quantity in terms of the indicated variable. The average of three test scores if the first two scores are 78 and \(82 ; \quad s=\) third test score

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ 3-2 x \leq \frac{1}{2} $$

Find the real and imaginary parts of the complex number. $$ \frac{-2-5 i}{3} $$

1–54 ? Find all real solutions of the equation. $$ x^{6}-81 x^{2}=0 $$

Solve the equation by factoring. \(x^{2}-7 x+12=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{1-[2-(3-x)]=4 x-(6+x)} \\ {\text { (a) } x=2 \quad \text { (b) } x=4}\end{array} $$

Solve the equation. $$ \frac{1}{2}|x|-7=2 $$

Express the given quantity in terms of the indicated variable. The average of four quiz scores if each of the first three scores is \(8 ; \quad q=\) fourth quiz score

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ 2 x-1 \geq x $$

Find the real and imaginary parts of the complex number. $$ \frac{4+7 i}{2} $$

1–54 ? Find all real solutions of the equation. $$ x^{5}-16 x=0 $$

Solve the equation by factoring. \(x^{2}+8 x+12=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{\frac{1}{x}-\frac{1}{x-4}=1} \\ {\begin{array}{ll}{\text { (a) } x=2} & {\text { (b) } x=4}\end{array}}\end{array} $$

Solve the equation. $$ |x-3|=2 $$

Express the given quantity in terms of the indicated variable. The interest obtained after one year on an investment at 2\(\frac{1}{2} \%\) simple interest per year; \(x=\) number of dollars invested

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ 1<2 x-4 \leq 7 $$

Find the real and imaginary parts of the complex number. $$ 3 $$

1–54 ? Find all real solutions of the equation. $$ x^{5}+8 x^{2}=0 $$

Solve the equation by factoring. \(3 x^{2}-5 x-2=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{2 x^{1 / 3}-3=1} \\ {\begin{array}{ll}{\text { (a) } x=-1} & {\text { (b) } x=8}\end{array}}\end{array} $$

Solve the equation. $$ |2 x-3|=7 $$

Express the given quantity in terms of the indicated variable. The total rent paid for an apartment if the rent is \(\$ 795\) a month; \(n=\) number of months

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ -2 \leq 3-x<2 $$

Find the real and imaginary parts of the complex number. $$ -\frac{1}{2} $$

1–54 ? Find all real solutions of the equation. $$ x^{4}+64 x=0 $$

Solve the equation by factoring. \(4 x^{2}-4 x-15=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{\frac{x^{3 / 2}}{x-6}=x-8} \\ {\begin{array}{ll}{\text { (a) } x=4} & {\text { (b) } x=8}\end{array}}\end{array} $$

Solve the equation. $$ |x+4|=0.5 $$

Express the given quantity in terms of the indicated variable. The area (in \(\mathrm{ft}^{2} )\) of a rectangle that is three times as long as it is wide; \(w=\) width of the rectangle (in \(\mathrm{ft} )\)

\(1-8=\) Let \(S=\left\\{-2,-1,0, \frac{1}{2}, 1, \sqrt{2}, 2,4\right\\} .\) Determine which elements of \(S\) satisfy the inequality. $$ \frac{1}{x} \leq \frac{1}{2} $$

Find the real and imaginary parts of the complex number. $$ -\frac{2}{3} i $$

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

Solve the equation by factoring. \(2 y^{2}+7 y+3=0\)

\(1-8\) Determine whether the given value is a solution of the equation. $$ \begin{array}{l}{\frac{x-a}{x-b}=\frac{a}{b} \quad(b \neq 0)} \\\ {\begin{array}{ll}{\text { (a) } x=0} & {\text { (b) } x=b}\end{array}}\end{array} $$

Express the given quantity in terms of the indicated variable. The perimeter (in \(\mathrm{cm} )\) of a rectangle that is 5 \(\mathrm{cm}\) longer than it is wide; \(w=\) width of the rectangle (in \(\mathrm{cm} )\)