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

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

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 each situation.

six times the quantity two x plus three y

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, write the exponent for the given expression.

$$9 \times 9 \times 9 \times 9$$

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.

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

Jenna is baking two different types of cookies. One recipe requires 3/4 cup of flour. The other recipe requires 1/2 cup of flour. She has 2 cups of flour. Is this enough flour to make both recipes? Explain how you know.

Which expressions in the table are equivalent?

Yolanda is planning a party that will take place in three rooms. The expression below can be used to represent the total amount Yolanda will need to rent all three rooms for t hours. Let t=5.

$$(25 t+15)+(20 t+10)+50 t$$

Explain how you can evaluate your expression and find the total rental cost Yolanda will pay. Then solve.

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

$$12 x-10-6 x$$

a. $6 x-10$

b. $2(3 x-5)$

c. $16 x-8-2$

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

twice a number n

Choose the best term from the Word List. Write it on the blank.

Word List

• algebraic expression
• base
• coefficient
• equivalent expressions
• evaluate
• exponent
• formula
• like terms
• power
• simplify
• substitution
• terms

A _____ is a quantity that can change or vary.