Chapter 2

In Exercises \(25-32\), simplify the expression by combining like terms. $$ 10 x-6-5 x $$

In Exercises 19-36, expand the expression as a product of factors. $$ 2(x z)^{4} $$

In Exercises 27-32, solve the equation. $$ 3 x=30 $$

In Exercises \(25-32\), simplify the expression by combining like terms. $$ 5 r+6-2 r+1 $$

In Exercises 19-36, expand the expression as a product of factors. $$ (x+y)^{2} $$

In Exercises 27-32, solve the equation. $$ \frac{3}{2} x=9 $$

In Exercises \(25-32\), simplify the expression by combining like terms. $$ 2 t-4+8 t+9 $$

In Exercises 19-36, expand the expression as a product of factors. $$ (s-t)^{5} $$

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} x-8 &=3 \\ x-8+8 &=3+8 \\ x &=11 \end{aligned} $$

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ 2(6 x) $$

In Exercises 19-36, expand the expression as a product of factors. $$ \left(\frac{a}{3 s}\right)^{4} $$

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} x+4 &=16 \\ x+4-4 &=16-4 \\ x &=12 \end{aligned} $$

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ -7(5 a) $$

In Exercises 19-36, expand the expression as a product of factors. $$ \left(-\frac{2}{5 x}\right)^{3} $$

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} \frac{2}{3} x &=12 \\ \frac{3}{2}\left(\frac{2}{3} x\right) &=\frac{3}{2}(12) \\ x &=18 \end{aligned} $$

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ -(4 x) $$

In Exercises 19-36, expand the expression as a product of factors. $$ \left[2(a-b)^{3}\right]\left[2(a-b)^{2}\right] $$

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} \frac{4}{5} x &=-28 \\ \frac{5}{4}\left(\frac{4}{5} x\right) &=\frac{5}{4}(-28) \\ x &=-35 \end{aligned} $$

In Exercises 23-36, write a verbal description of the algebraic expression, without using a variable. (There is more than one correct answer.) $$ x^{3}-1 $$

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ -(5 t) $$

In Exercises 19-36, expand the expression as a product of factors. $$ \left[3(r+s)^{2}\right][3(r+s)]^{2} $$

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} 5 x+12 &=22 \\ 5 x+12-12 &=22-12 \\ 5 x &=10 \\ \frac{5 x}{5} &=\frac{10}{5} \\ x &=2 \end{aligned} $$

The sales tax on a purchase of \(L\) dollars is \(6 \%\). Write an algebraic expression that represents the total amount of sales tax. (Hint: Use the decimal form of \(6 \%\).)

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ (-2 x)(-3 x) $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(2 x-1\) (a) \(x=\frac{1}{2}\) (b) \(x=-4\)

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} 14-3 x &=5 \\ 14-3 x-14 &=5-14 \\ 14-14-3 x &=5-14 \\ -3 x &=-9 \\ \frac{-3 x}{-3} &=\frac{-9}{-3} \\ x &=3 \end{aligned} $$

The state income tax on a gross income of \(I\) dollars in Pennsylvania is \(3.07 \%\). Write an algebraic expression that represents the total amount of income tax.

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ (-3 y)(-4 y) $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(3 x-2\) (a) \(x=\frac{4}{3}\) (b) \(x=-1\)

In Exercises 39-42, write an algebraic equation. Do not solve the equation. After your instructor added 6 points to each student's test score, your score is 94 . What was your original score?

A movie rental costs \(\$ 3\) per day. A video game rental costs \(\$ 4\) per day. Write an algebraic expression that represents the total cost of renting \(m\) movies and \(v\) video games per day.

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ (-5 z)\left(2 z^{2}\right) $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(2 x^{2}-5\) (a) \(x=2\) (b) \(x=3\)

In Exercises 39-42, write an algebraic equation. Do not solve the equation. With the \(1.2\)-inch rainfall today, the total for the month is \(4.5\) inches. How much had been recorded for the month before today's rainfall?

The height of a rectangular picture frame is \(1.5\) times the width \(w\). Write an algebraic expression that represents the perimeter of the picture frame.

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ (10 t)\left(-4 t^{2}\right) $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(64-16 t^{2}\) (a) \(t=2\) (b) \(t=3\)

In Exercises 39-42, write an algebraic equation. Do not solve the equation. During a football game, a running back carried the ball 18 times and his average number of yards per carry was \(4.5\). How many yards did the running back gain for the game?

An employee's hourly wage is \(\$ 12.50\) per hour plus \(\$ 0.75\) for each of the \(q\) units produced during the hour. Write an algebraic expression that represents the employee's total hourly earnings.

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ \frac{18 a}{5} \cdot \frac{15}{6} $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(3 x-2 y\) (a) \(x=4, y=3\)

In Exercises 39-42, write an algebraic equation. Do not solve the equation. The total cost of admission for 6 adults at an aquarium is \(\$ 132\). What is the cost per adult?

A campground charges \(\$ 15\) for adults and \(\$ 2\) for children. Write an algebraic expression that represents the total camping fee for \(m\) adults and \(n\) children,

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ \frac{5 x}{8} \cdot \frac{16}{5} $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(10 u-3 v\) (a) \(u=3, v=10\) (b) \(u=-2, v=\frac{4}{7}\)

You want to volunteer at a soup kitchen for 150 hours over a 15 -week period. After 8 weeks, you have volunteered for 72 hours. How many hours will you have to work per week over the remaining 7 weeks to reach your goal?

Applications for a cellular phone cost \(\$ 0.99\) each. Ringtones cost \(\$ 1.99\) each. Write an algebraic expression that represents the total cost of buying \(a\) applications and \(r\) ringtones.

$$ \text { In Exercises 33-46, simplify the expression. } $$ $$ \left(-\frac{3 x^{2}}{2}\right)\left(\frac{4 x}{18}\right) $$

In Exercises 37-44, evaluate the algebraic expression for the given values of the variable(s). \(x-3(x-y)\) (a) \(x=3, y=3\) (b) \(x=4, y=-4\)

A textile corporation buys equipment with an initial purchase price of \(\$ 750,000\). It is estimated that its useful life will be 3 years and at that time its value will be \(\$ 75,000\). The total depreciation is divided equally among the three years. (Depreciation is the difference between the initial price of an item and its current value.) What is the total amount of depreciation declared each year?