Equations and Inequalities on Both Sides

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

Select the situation that could be modeled by: 12 + 5x = 18+3x

• Derek charges a base fee of $12 to walk a dog plus $5 per hour. Darla charges a base fee of $18 plus $3 an hour to walk a dog. After how many hours would they make the same amount of money?

• Andy buys 12 sodas for $5 each. Alex buys 18 sodas for $3 each. If they each spent the same amount, how much did they spend?

• Brian charges $12 for a hat and $5 per shirt. Blake buys 3 hats and 18 shirts. How many hats and shirts must they sell to make the same amount of money?

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x

• 30x + 20 < 15x + 30

• 30 + 20x > 15 + 30x

• 30x + 20 > 15x + 30

Choose the situation that could represent the inequality:
25 – x < 15 + x

• Kasey has a gift card for $25. She buys a $15 CD and as many decals as she can buy with the rest of the gift card. How many decals can she buy?

• The school band has 25 people, and the theater class has 15 people. How many people must move from the band class to the theater class for the theater class to be as big or larger than the school band?

What inequality symbol is used in:
384 + 2x < 6x?

• Greater Than

• Less Than

• Greater Than or Equal To

• Less Than or Equal To

Select the situation that could be modeled by: 2x + 4 = 3x

• The number of students in the 2-year-old class and the 4-year-old class equals the number of students in the 3-year-old class. How many students are in each class?

• Cade bought 2 books for $4 each and Clara bought 3 books. How much did Clara pay?

• Dean is 4 more than twice his brother’s age. He is also 3 times his brother’s age. How old is Dean’s brother?

• a ≥ 4
• a ≥ -4
• a ≤ 4
• a ≤ -4

Solve for f:
f - 4 = 6f + 26

• f = -5

• f = 5

• f = 6

• f = -6

Solve for x:
5x - 14 = 8x + 4

• x = 6

• x = -6

• x = -18/13

• x = 10/3

Solve the equation
4x - 5x + 9 =5x - 9

• x = -3

• x = 9

• x = 3

• x = -9