Algebra Practice

The steps used to solve the equation 2x+8=20 for x are shown below:

2x+8=20

Step 1: 2x=12

Step 2: x=6

Which property makes Step 1 true?

• Division property of equality

• Reflexive property of equality

• Subtraction property of equality

• Symmetric property of equality

The steps used to solve the equation 2x+8=20 for x are shown below:

2x+8=20

Step 1: 2x=12

Step 2: x=6

Which property makes Step 2 true?

• Division property of equality

• Reflexive property of equality

• Subtraction property of equality

• Symmetric property of equality

Guests who rent canoes must pay an insurance fee and are charges for each hour they use the canoe. Last year, the total cost for a guest to rent a canoe for x hours was modeled by the expression 6+8x. This year, they are doubling the cost per hour for renting a canoe but kept the insurance fee the same. Which expression models the total cost for a guest to rent a canoe for x hours this year?

• 12+8x

• 6+16x

• 6+4x

• 3+8x

Which expression represents the area of the rectangle shown?

A bag contains n nickels and q quarters worth a total of $40.

Which equation models this information?

• n+q=40

• 5n+25q=40

• 0.5n+0.25q=40

• 0.05n+0.25q=40

On what interval of x-values is the function g(x) increasing?

• (-3,6)

• (0,3)

• (1,10)

• (6,10)

The manager of the R&B group budgeted $1800 to buy souvenir clothing to sell at the venue. She can buy shirts for $10 each and hats for $8 each. She plans to buy at least 5 times as many shirts as hats. The manager used these inequalities to determine the number of shirts, s, and hats, h, that can be ordered. What error did the manager make?

• the inequalities should be equations

• the first inequality should be

  10s+8h>1800

• the second inequality should be s>5h

• the first inequality should be s+h<1800

Which of these points lies on the graph of the equation x-12=y?

• (4,8)

• (3,15)

• (-4,-8)

• (-2,-14)

Juan and Nia are each solving the equation 13x-42=18-7x. Juan's first step was to rewrite the equations as 20x-42=18 while Nia's first step was to rewrite the equation as 13x=60-7x. Who is correctly applying the addition property of equality in the first step of his work?

• Only Juan

• Only Nia

• Both Nia and Juan

• Neither Nia and Juan

What are the variable(s) in this expression?
6g⁴ + 5h³ + j - 90

• g, h, j

• 6, 5, 1

• 4, 3

• 90