Chapter 1

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

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

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

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

Solve the equation. $$ |4 x+7|=9 $$

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

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

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

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

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 2 x+7=31 $$

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

Express the given quantity in terms of the indicated variable. The time (in hours) it takes to travel a given distance at \(55 \mathrm{mi} / \mathrm{h} ; \quad d=\) given distance (in mi)

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -4 x \geq 10 $$

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

1–54 ? Find all real solutions of the equation. $$ (x-2)^{5}-9(x-2)^{3}=0 $$

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

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

Solve the equation. $$ 4-|3 x+6|=1 $$

Express the given quantity in terms of the indicated variable. The concentration (in oz/gal) of salt in a mixture of 3 gal of brine containing 25 oz of salt, to which some pure water has been added; \(x=\) volume of pure water added (in gal)

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x-5>3 $$

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

1–54 ? Find all real solutions of the equation. $$ x^{3}-5 x^{2}-2 x+10=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{1}{2} x-8=1 $$

Solve the equation. $$ |5-2 x|+6=14 $$

Express the given quantity in terms of the indicated variable. The value (in cents) of the change in a purse that contains twice as many nickels as pennies, four more dimes than nickels, and as many quarters as dimes and nickels combined; \(p=\) number of pennies

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 3 x+11<5 $$

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

1–54 ? Find all real solutions of the equation. $$ 2 x^{3}+x^{2}-18 x-9=0 $$

Solve the equation by factoring. \(6 x(x-1)=21-x\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 3+\frac{1}{3} x=5 $$

Solve the equation. $$ 3|x+5|+6=15 $$

Number Problem Find three consecutive integers whose sum is \(156 .\)

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 7-x \geq 5 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (-6+6 i)+(9-i) $$

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

Solve the equation by completing the square. \(x^{2}+2 x-5=0\)

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

Solve the equation. $$ 20+|2 x-4|=15 $$

Number Problem Find four consecutive odd integers whose sum is 416 .

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 5-3 x \leq-16 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (3-2 i)+\left(-5-\frac{1}{3} i\right) $$

1–54 ? Find all real solutions of the equation. $$ 7 x^{3}-x+1=x^{3}+3 x^{2}+x $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 4 x+7=9 x-13 $$

Solve the equation. $$ 8+5\left|\frac{1}{3} x-\frac{5}{6}\right|=33 $$

Investments Phyllis invested \(\$ 12,000,\) a portion earning a simple interest rate of 4\(\frac{1}{2} \%\) per year and the rest earning a rate of 4\(\%\) per year. After one year the total interest earned on these investments was \(\$ 525 .\) How much money did she invest at each rate?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x+1<0 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ \left(7-\frac{1}{2} i\right)-\left(5+\frac{3}{2} i\right) $$