Solving and Writing Equations and Inequalities Vocabulary

Solve.
½x - 6 = ¼x + 4

• s = -40

• s= 40

• s=20

• s= -20

Select the situation that could be modeled by: 120 + 25x = 45x.

• John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?

• George charges a flat fee of $120 to mow a lawn plus $25 an hour. Greg charges $45 a hour to mow a lawn. After how many hours do they make the same amount?

• Lisa pays $120 for each purse she buys plus an additional $25 to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

• A cell phone company charges $25 for service and $120 per gigabyte.  Another company charges $45 per gigabyte.  For how many gigabytes would the price be the same?

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?

• Charlie sells dozens of eggs for $5.  Calvin sells a dozen and a half eggs for $3 each.  How many do they have to sell to make the same amount of money?

Solve.
.5x - 1 = .25x + 2

• x = 3

• x = -12

• x = 12

• x = -3

Which inequality represents the following problem:
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. Find the number of square yards of carpet for The Rug Store charges 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

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?

• A shirt is on sale for $25, but Garrett has a coupon for some money off.  His sister Grace buys 15 of the same shirt so he will never lose it.  How much does the shirt cost?

• Every time Ashley goes to Starbucks, it takes $4 off her $25 gift card.  Amanda uploads $15 more to her gift card.  How much does Amanda add to have more than Ashley?

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

Label the inequality symbol: >

• Less Than

• Greater Than

• Less Than or Equal To

• Greater Than or Equal to

Solve.
⅓x + 10 = ¾x + 5

• x = 1

• x = -1

• x = 12

• x = -12

Label the inequality symbol: <

• Less Than

• Greater Than

• Less Than or Equal To

• Greater Than or Equal to