Chapter 1

Determine whether the given value is a solution of the equation. \(\frac{1}{x}-\frac{1}{x-4}=1\) (a) \(x=2 \quad\) (b) \(x=4\)

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

\(5-22=\) Solve the equation. $$ |x-3|=2 $$

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

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

\(5-60\) Find all real solutions of the equation. $$ x^{5}+8 x^{2}=0 $$

\(7-18 \cdot\) 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

Determine whether the given value is a solution of the equation. \(2 x^{1 / 3}-3=1\) (a) \(x=-1 \quad\) (b) \(x=8\)

\(5-22=\) Solve the equation. $$ |2 x-3|=7 $$

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

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

\(5-60\) Find all real solutions of the equation. $$ x^{4}+64 x=0 $$

\(7-18 \cdot\) 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

Determine whether the given value is a solution of the equation. \(\frac{x^{3 / 2}}{x-6}=x-8\) (a) \(x=4 \quad\) (b) \(x=8\)

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

\(5-22=\) Solve the equation. $$ |x+4|=0.5 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x \leq 7 $$

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

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

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The interest obtained after one year on an investment at \(2^{1} \%\) simple interest per year; \(x=\) number of dollars invested

Determine whether the given value is a solution of the equation. \(\frac{X-a}{X-b}=\frac{a}{b} \quad(b \neq 0)\) (a) \(x=0 \quad\) (b) \(x=b\)

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

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -4 x \geq 10 $$

Solve the equation by factoring. $$ 4 w^{2}=4 w+3 $$

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

\(7-18 \cdot\) 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

Determine whether the given value is a solution of the equation. \(x^{2}-b x+\frac{1}{4} b^{2}=0\) (a) \(x=\frac{b}{2} \quad\) (b) \(x=\frac{1}{b}\)

Find the real and imaginary parts of the complex number. $$ \sqrt{3}+\sqrt{-4} $$

\(5-22=\) Solve the equation. $$ |4 x+7|=9 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x-5>3 $$

Solve the equation by factoring. $$ 6 x^{2}+5 x=4 $$

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

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The area \(\left(\text { in } \mathrm{ft}^{2}\right)\) of a rectangle that is three times as long as it is wide; \(\quad w=\) width of the rectangle (in \(\mathrm{ft} )\)

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(2 x+7=31\)

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

\(5-22=\) Solve the equation. $$ \left|\frac{1}{2} x-2\right|=1 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 3 x+11<5 $$

Solve the equation by factoring. $$ 3 x^{2}+1=4 x $$

\(5-60\) Find all real solutions of the equation. $$ (x-2)^{5}-9(x-2)^{3}=0 $$

\(7-18 \cdot\) 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 \(\mathrm{cm} )\)

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

Evaluate the expression and write the result in the form a bi. $$ (2-5 i)+(3+4 i) $$

\(5-22=\) Solve the equation. $$ 4-|3 x+6|=1 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 7-x \geq 5 $$

Solve the equation by factoring. $$ x^{2}=5(x+100) $$

\(5-60\) Find all real solutions of the equation. $$ x^{3}-5 x^{2}-2 x+10=0 $$

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The distance (in mi) that a car travels in 45 min; \(s=\) speed of the car (in \(\mathrm{mi} / \mathrm{h} )\)

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{1}{2} x-8=1\)

Evaluate the expression and write the result in the form a bi. $$ (2+5 i)+(4-6 i) $$

\(5-22=\) Solve the equation. $$ |5-2 x|+6=14 $$