Equations and Inequalities

Which situation is best represented by the equation 2 + 1.5x = 2x ?

Billy's movie club charges a membership fee of $2 plus $1.50 per rental, while Suzie's movie club has no membership fee but charges $2 per rental. Billy and Suzie find that they each rented the same number of movies last month and paid the same total amount. Find x, the number of movies each person rented.

Which scenario could be represented by the equation 80 + 10x = 70 + 12x ?

Caroline receives $80 for her birthday and earns $10 each time she babysits. Addison has saved $70 and earns $12 · each time she babysits. How many times must the girls babysit, x, so that Addison and Caroline make the same amount of money?

Which scenario could be represented by the inequality 80 + 10x > 70 + 12x ?

Cell phone company A charges an $80 deposit and $10 each month for unlimited service. Cell phone company B charges a $70 deposit and $12 each month for unlimited service. After how many months, x, will cell phone company A cost more than cell phone company B?

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Greater than

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Less than

Which scenario could be represented by the inequality 40 + 30x < 5Ox ?

Lila is looking into alarm systems for her home. Company A offers a plan that has an initial fee of $40 then charges $30 per month. Company 8 offers a plan that charges $50 per month. After how many months, x, will Company A cost less than Company 8?

Which scenario could be represented by the equation 35 - 5x = 50 - 15x ?

Mallory and Aimee spend money on summer camp. They both plan to spend the same amount of money. Mallory has $35 and plans to spend $5 each week. Aimee has $50 and plans to spend $15 each week. Which of the following can be used to determine x, the number of weeks it will take Mallory and Aimee to have the same amount of money?

Which scenario could be represented by the inequality 12x + 80 < 10x + 70 ?

Marco wants to rent a drum set. At Music World, the cost to rent drums is $12 per month plus an $80 deposit. Instrumental Music rents drums for $10 per month with a $70 deposit. How many months, x, can Marco rent drums from Music World and pay less than he will at Instrumental Music?

Which scenario could be represented by the inequality 40x + 30 < 50x ?

Regina purchases a new cell phone. Her first option is to purchase a plan that charges $40 per month, and she receives a phone for $30. The second P.lan charges $50 per month, and she receives the phone for free. After how many months, x, will the first option cost less than the second option?

Which scenario could be represented by the equation 5.5 + 0.4x = 6. 75 + 0.35x ?

Two shipping companies charge different amounts to ship a package. Company A charges $5.50 for the first pound and $0.40 for each additional pound. Company B charges $6.75 for the first pound and $0.35 for each additional pound. If the cost to ship a package is the same for both companies, what is the weight in pounds, x, of the package?

variable

a letter that is used to represent an unkown number

Inequality

mathematical sentence than compares expressions

equation

mathematical sentence that uses and equal sign to show that two expressions have the same value