91Ó°ÊÓ

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

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.

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?

You buy \(t\) tickets to a baseball game for a total of \(\$ 45\). Write an algebraic expression that represents the cost of each ticket.

The dimensions of a rectangular lawn are 150 feet by 250 feet. The property owner buys a rectangular strip of land \(x\) feet wide along one 250 -foot side of the lawn. Draw diagrams representing the lawn before and after the purchase. Write an expression for the area of each.

In Exercises \(55-58\), write an algebraic equation. Do not solve the equation. A school science club conducts a car wash to raise money. The club spends \(\$ 12\) on supplies and charges \(\$ 5\) per car. After the car wash, the club has a profit of \(\$ 113\). How many cars did the members of the science club wash?

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 3-2[6+(4-x)] $$

What is a hidden operation in a verbal phrase? Explain how to identify hidden operations.

In Exercises \(63-68\), simplify the expression. $$ \left(-3 y^{3}\right) y^{2} $$

In Exercises \(63-68\), simplify the expression. $$ 4-3 t+t $$