Chapter 1

Evaluate \(x^{2}-2 x+2\) for \(x=1+i\)

Solve each equation in by making an appropriate substitution. $$ \left(y-\frac{8}{y}\right)^{2}+5\left(y-\frac{8}{y}\right)-14=0 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ x^{2}+5 x+3=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=l w\) for \(w\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|x|<3$$

In Exercises \(51-58,\) determine whether each equation is an identity, a conditional equation, or an inconsistent equation. $$ \frac{2 x}{x-3}=\frac{6}{x-3}+4 $$

Solve each equation in by making an appropriate substitution. $$ \left(y-\frac{10}{y}\right)^{2}+6\left(y-\frac{10}{y}\right)-27=0 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ x^{2}+5 x+2=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(D=R T\) for \(R\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|x|<5$$

In Exercises \(51-58,\) determine whether each equation is an identity, a conditional equation, or an inconsistent equation. $$ \frac{3}{x-3}=\frac{x}{x-3}+3 $$

Writing in Mathematics What is a quadratic inequality?

Solve each absolute value equation or indicate the equation has no solution. $$ |x|=8 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ 3 x^{2}-3 x-4=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} b h\) for \(b\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|x-1| \leq 2$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ \frac{x+5}{2}-4=\frac{2 x-1}{3} $$

What is a rational inequality?

Which one of the following is true? a. If the coordinates of a point satisfy the inequality \(x y>0,\) then \((x, y)\) must be in quadrant I. b. The ordered pair \((2,5)\) satisfies \(3 y-2 x=-4\) c. If a point is on the \(x\) -axis, it is neither up nor down, so \(x=0\) d. None of the above is true.

Solve each absolute value equation or indicate the equation has no solution. $$ |x|=6 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ 5 x^{2}+x-2=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(V=\frac{1}{3} B h\) for \(B\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|x+3| \leq 4$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ \frac{x+2}{7}=5-\frac{x+1}{3} $$

Describe similarities and differences between the solutions of $$ (x-2)(x+5) \geq 0 \text { and } \frac{x-2}{x+5} \geq 0 $$

Solve each absolute value equation or indicate the equation has no solution. $$ |x-2|=7 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ 4 x^{2}=2 x+7 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(I=P r t\) for \(P\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|2 x-6|<8$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ \frac{2}{x-2}=3+\frac{x}{x-2} $$

Solve each absolute value equation or indicate the equation has no solution. $$ |x+1|=5 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ 3 x^{2}=6 x-1 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(C=2 \pi r\) for \(r\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|3 x+5|<17$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ \frac{6}{x+3}+2=\frac{-2 x}{x+3} $$

Solve each inequality in Exercises \(62-65\) using a graphing utility. $$ 2 x^{2}+5 x-3 \leq 0 $$

Solve each absolute value equation or indicate the equation has no solution. $$ |2 x-1|=5 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ x^{2}-6 x+10=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(E=m c^{2}\) for \(m\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|2(x-1)+4| \leq 8$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ 8 x-(3 x+2)+10=3 x $$

Solve each absolute value equation or indicate the equation has no solution. $$ |2 x-3|=11 $$

Solve each equation in Exercises \(55-64\) using the quadratic formula. $$ x^{2}-2 x+17=0 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 64\. \(V=\pi r^{2} h\) for \(h\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$|3(x-1)+2| \leq 20$$

The equations in Exercises \(59-70\) combine the types of equations we have discussed in this section. Solve each equation or state that it is true for all real numbers or no real numbers. $$ 2(x+2)+2 x=4(x+1) $$

Compute the discriminant of each equation in Exercises 65-72 What does the discriminant indicate about the number and type of solutions? \(x^{2}-4 x-5=0\)

Solve each absolute value equation or indicate the equation has no solution. $$ 2|3 x-2|=14 $$

In Exercises \(57-76,\) solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(T=D+p m\) for \(p\)

Solve each inequality in Exercises 57-84 by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$\left|\frac{2 y+6}{3}\right|<2$$