In the following exercise, identify which expressions are equivalent to the given expression.

$$\frac{1}{2} x+3+\frac{1}{2} x$$

a. $\frac{1}{2}(x+3)$

b. $x+3$

c. $3 x+3-x$

The same digits are used for the expressions $3^4$ and $4^3$. Explain how to compare the value of each expression.

Mrs. Hayes hired Alex and Tyrone to build doghouses for her kennel service. She paid each worker a daily overtime bonus and an hourly wage. The project took two days to complete. Mrs. Hayes used the algebraic expression $2(10+7 x)+2(15+8 x)$ to calculate the total amount she paid Alex and Tyrone for working $x$ hours on each of the two days.

How are each worker's earnings represented in the expression? Explain how you know.

In the following exercise, evaluate the given expression.

$$[(7.3+3.6)-4.7]+1.8-2^2$$

Josephine's math study group is doing a research project. There are 5 students in her group. In January, each group member surveyed x volunteers and gave a 10-minute presentation. Each volunteer completed a follow-up survey in May. Josephine wrote the expression $5(6 x+25 x+10)$ to represent the total time in minutes that her group spent surveying volunteers and giving presentations.

How can you use properties of operations to write an equivalent expression? Explain your reasoning.

In the following exercise, use properties of operations to complete the equivalent expression.

$5(3 x-9)$ and $\underline{\quad}x-\underline{\quad}$

Evaluate the following numerical expression.

$$94-(5 \times 6) \div 6 \times 11$$

In the following, complete each table. Then circle the expressions that are equivalent.

Draw a line from each expression in Column A to an equivalent expression in Column B.

$$\begin{array}{} \text{Column A} &&&&&&&&&\text{Column B}\\ 3 x+2 &&&&&&&&& 6x\\ &&&&&&&&&4(x-2)\\ &&&&&&&&&6x-9\\ &&&&&&&&&4x+3-x-1\\ \end{array}$$

Simplify the given expression.

$$y^2+3 y^2$$

In the following exercise, use the expression $1+\frac{z}{3}+2 w$.

Which part of the expression is a quotient? Describe its parts.

In the following exercise, simplify the given expression.

4y-y

In the following exercise, write the exponent for the given expression.

$$\left(\frac{2}{3}\right)^8$$

In the following exercise, write an algebraic expression for the given situation.

12 fewer than h hats