Chapter 1

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ 0 . \overline{016} \quad \frac{2}{125} $$

\(\quad\) A retired teacher has a choice of two investment plans: An insured fund that pays \(11 \%\) interest A risky investment that pays a \(13 \%\) return If the same amount invested at the higher rate would general an extra \(\$ 150\) per year than it would at the lower rate, how much does the teacher have to invest?

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 10. $$ 5(y+2)+7-3 y=2(y+9) $$

Simplify by combining like terms. See Example 5 . $$\frac{3}{16} x-\frac{5}{4} x$$

Solve for the specified variable. $$ s=v_{0} t-16 t^{2} \quad \text { for } v_{0} $$

Evaluate each expression. See Example \(9 .\) $$ (-1-\sqrt{144})^{2} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ 1 . \overline{1875} \quad \frac{19}{16} $$

Solve each equation. $$ \frac{3}{4} x-5=\frac{2}{3} x+\frac{1}{4} $$

Simplify by combining like terms. See Example 5 . $$-9 a+11 a d-35 a+a d$$

Solve for the specified variable. $$ G=U-T S+p V \quad \text { for } S $$

Evaluate each expression. See Example \(9 .\) $$ -2|4-8| $$

Find the value of each expression. $$ |20| $$

Solve each equation. $$ \frac{3}{5} x+\frac{7}{10}=x-\frac{4}{5} $$

Simplify by combining like terms. See Example 5 . $$-7 a+2 a b-7 a+12 a b$$

Solve for the specified variable. $$ F=\frac{G m_{1} m_{2}}{r^{2}} \quad \text { for } m_{1} $$

Evaluate each expression. See Example \(9 .\) $$ |\sqrt{49}-8(4-7)| $$

Find the value of each expression. $$ |-20| $$

Simplify by combining like terms. See Example 5 . $$4 m-t-(-2 m)+3 t$$

Solve each equation. $$ 8 x=x $$

Solve for the specified variable. $$ P V=n r t \quad \text { for } r $$

Evaluate each expression. See Example \(9 .\) $$ 2+3\left(\frac{25}{5}\right)+(-4) $$

Find the value of each expression. $$ |-5.9| $$

Solve each equation. $$ -z=5 z $$

Solve for the specified variable. $$ P=s_{1}+s_{2}+b \quad \text { for } s_{2} $$

Evaluate each expression. See Example \(9 .\) $$ (-2)^{3}\left(\frac{-6}{-2}\right)(-1) $$

Find the value of each expression. $$ -|1 . \overline{27}| $$

Simplify. See Example \(6 .\) $$2 x^{2}+4\left(3 x-x^{2}\right)+3 x$$

Solve each equation. $$ -x+12=-17 $$

Solve for the specified variable. $$ E=I R+I r \quad \text { for } R $$

Find the value of each expression. $$ -|-6| $$

Simplify. See Example \(6 .\) $$3 p^{2}-6\left(5 p^{2}+p\right)+p^{2}$$

Solve each equation. $$ 6=-x+41 $$

Solve for the specified variable. $$ A x+B y=C \quad \text { for } x $$

Find the value of each expression. $$ -|-8| $$

Simplify. See Example \(6 .\) $$-3(p-2)+2(p+3)-5(p-1)$$

Solve each equation. $$ \frac{1}{2} b-\frac{19}{6}=\frac{1}{3} b+\frac{5}{6} $$

Solve for the specified variable. $$ A=\frac{1}{3}\left(s_{1}+s_{2}+s_{3}\right) \quad \text { for } s_{3} $$

Find the value of each expression. $$ -\left|\frac{9}{4}\right| $$

Simplify. See Example \(6 .\) $$5(q+7)-3(q-1)-(q+2)$$

Solve each equation. $$ \frac{1}{2} w-\frac{7}{6}=\frac{53}{6}-\frac{1}{3} w $$

Solve for the specified variable. $$ P_{1} V_{1} T_{2}=P_{2} V_{2} T_{1} \quad \text { for } V_{2} $$

Find the value of each expression. $$ -\left|-\frac{5}{16}\right| $$

Simplify. See Example \(6 .\) $$36\left(\frac{2}{9} x-\frac{3}{4}\right)+36\left(\frac{1}{2}\right)$$

Solve each equation. $$ a+18=5 a-3+a $$

Solve for the specified variable. $$ S=\frac{n}{2}[2 a+(n-1) d] \quad \text { for } d $$

Evaluate each expression. See Example \(9 .\) $$ \frac{1}{3}\left(\frac{1}{6}\right)-\left(-\frac{1}{3}\right)^{2} $$

Simplify. See Example \(6 .\) $$40\left(\frac{3}{8} y-\frac{1}{4}\right)+40\left(\frac{4}{5}\right)$$

Solve each equation. $$ 4 a-21-a=-2 a-7 $$

Solve for the specified variable. $$ x^{2}=4 p y \quad \text { for } p $$

Evaluate each expression. See Example \(9 .\) $$ \frac{1}{2}\left(\frac{1}{8}\right)+\left(-\frac{1}{4}\right)^{2} $$