Chapter 1

Solve each compound inequality. $$-6 \leq \frac{1}{2} x-4<-3$$

By making an appropriate substitution. $$\left(x^{2}-2 x\right)^{2}-11\left(x^{2}-2 x\right)+24=0$$

Find all values of \(x\) such that \(y=0\). \(y=2[3 x-(4 x-6)]-5(x-6)\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=P r t \text { for } P$$

Explain how to add complex numbers. Provide an example with your explanation.

Solve each equation in Exercises \(47-64\) by completing the square. $$ 2 x^{2}-7 x+3=0 $$

Solve each absolute value inequality. $$|x|<3$$

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

Find all values of \(x\) such that \(y=0\). \(y=\frac{x+6}{3 x-12}-\frac{5}{x-4}-\frac{2}{3}\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$C=2 \pi r \text { for } r$$

Explain how to multiply complex numbers and give an example.

Solve each equation in Exercises \(47-64\) by completing the square. $$ 2 x^{2}+5 x-3=0 $$

Solve each absolute value inequality. $$|x|<5$$

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

Find all values of \(x\) such that \(y=0\). \(y=\frac{1}{5 x+5}-\frac{3}{x+1}+\frac{7}{5}\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$E=m c^{2} \text { for } m$$

What is the complex conjugate of \(2+3 i ?\) What happens when you multiply this complex number by its complex conjugate?

Solve each equation in Exercises \(47-64\) by completing the square. $$ 4 x^{2}-4 x-1=0 $$

Solve each absolute value inequality. $$|x-1| \leq 2$$

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

What is the rectangular coordinate system?

Solve equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. \(5 x+9=9(x+1)-4 x\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=\pi r^{2} h \text { for } h$$

Explain how to divide complex numbers. Provide an example with your explanation.

Solve each equation in Exercises \(47-64\) by completing the square. $$ 2 x^{2}-4 x-1=0 $$

Solve each absolute value inequality. $$|x+3| \leq 4$$

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

Solve equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. \(4 x+7=7(x+1)-3 x\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$T=D+p m \text { for } p$$

Solve each equation in Exercises \(47-64\) by completing the square. $$ 3 x^{2}-2 x-2=0 $$

Solve each absolute value inequality. $$|2 x-6|<8$$

Explain why \((5,-2)\) and \((-2,5)\) do not represent the same point.

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

Solve equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. \(3(x+2)=7+3 x\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$P=C+M C \text { for } M$$

A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached an imaginary number. Please multiply by \(i\) and dial again." Explain the joke.

Solve each equation in Exercises \(47-64\) by completing the square. $$ 3 x^{2}-5 x-10=0 $$

Solve each absolute value inequality. $$|3 x+5|<17$$

Explain how to graph an equation in the rectangular coordinate system.

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

Solve equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. \(4(x+5)=21+4 x\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=\frac{1}{2} h(a+b) \text { for } a$$

Explain the error $$ \sqrt{-9}+\sqrt{-16}=\sqrt{-25}=i \sqrt{25}=5 i $$

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$ x^{2}+8 x+15=0 $$

Solve each absolute value inequality. $$|2(x-1)+4| \leq 8$$

What does a \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle mean?

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

Solve equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. \(10 x+3=8 x+3\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$A=\frac{1}{2} h(a+b) \text { for } b$$

Solve each equation in Exercises \(65-74\) using the quadratic formula. $$ x^{2}+8 x+12=0 $$