/ Class:
/ Date:
7th Grade PreAP Expressions, Equations, and Inequalities Review WS
Indicate the answer choice that best completes the statement or answers the question.Solve the equation. Check your solution.
1. 6p –20 = 22
Translate each sentence into an equation. Then find each number.
2.The difference between four times a number and six is –46.
Equation:______
Solution: ______
3.The sum of eleven and seven times a number is –17.Equation:______
Solution: ______
Solve each problem by writing and solving an equation.4.Amelia decided to order breadsticks and a pizza. The pizza cost $10.50 and each breadstick costs $0.75. If Amelia’s bill was $13.50, how many breadsticks did Amelia order?
Equation:______
Solution: ______
5.You and two of your friends go to the movies. Each ticket costs $7.50. You share the cost of the popcorn. If each person pays $9.05, how much was the popcorn?
Equation:______
Solution: ______
Solve each equation. Check your solution.6.15g –5 = 14g
7.7h – 7 = 5h + 13
8.Mrs. Carrie had 3 leftover apple pies. She gave 5 pies to her brother. Her daughter took 9 home with her. How many pies did Mrs. Carrie bake at the beginning?
9.A red hot air balloon is at an altitude of260feet above the ground. It is descending at a rate of9feet per minute. A green hot air balloon is at an altitude of75feet and is ascending at a rate of7feet per minute. Which inequality represents the number of minutes it will take for the green hot air balloon to have a greater altitude than the red hot air balloon?
a. / 260–9m75+7m / b. / 260–9m <75+7m
c. / 260+9m75–7m / d. / 260–7m75+9m
10.An online movie rental club charges a membership fee of $18.95plus $3.35for each movie downloaded. Non-members can also download movies for $4.95each. Which inequality represents the number of movie downloads for which non-members would pay as much or more than members?
a. / 18.95+3.35n≥4.95n / b. / 3.35n≤18.95+4.95n
c. / 18.95+4.95n≤3.35n / d. / 18.95+3.35n≤4.95n
Write a real-world problem given the inequality.
11.
a. / US Cell charges a monthly fee of $12 and $0.25 for each text. National Cellular charges $0.10 a text. How many texts wouldUS Cell customers have to make in order for their monthly cost to be less than or equal to National Cellular?
b. / Maineville Bank offers an ATM card to its customers for an annual fee of $12 plus an additional charge of $0.10 per transaction. The Champion Credit Union offers an ATM card to its members with no annual fee and a charge of $0.25 per transaction. How many transactions would a Maineville Bank customer have to make in order for their total fees to be less than or the same as a Champion Credit Union member?
c. / Woodbridge Landscaping charges a one time fee of $12 per summer for lawnmower maintenance and $10 per half acre of grass cut. Oberson Landscaping charges $25 per half acre of grass cut. How many acres does a customer of Woodbridge Landscaping need to have cut for the cost to be less than or the same as an Oberson Landscaping customer?
d. / Marco earns $10 each week and an additional $0.12 per minute spent completing his chores. Sabrina earns $0.25 per minute spent completing her chores. How many minutes does Marco need to work to earn less than or equal to the amount Sabrina earns?
12.40 + 100x > 120 + 29x
a. / Briana opened a savings account with an initial deposit of $100 and deposits $40 each month into the account. Kumar opened a savings account on the same day with an initial deposit of $29 and deposits $120 each month. How many months will it take for Briana’s account to be greater than Kumar’s account?
b. / Cam is a personal trainer who charges a one-time evaluation fee of $40 and $100 a session. Ava charges a one time evaluation fee of $120 to her clients and $29 each session. How many sessions would a client need to have for Ava’s fees to be greater than Cam’s?
c. / Tyrone charges an initial fee of $40 plus $100 per hour when hired as a caterer for special events. Anders charges an initial fee of $120 plus $29 per hour when hired. How many hours does Tyrone need to work in order to make more money than Anders?
d. / Mainer Tree Nursery charges $100 per tree and $40 per tree for delivery. Emerald Tree Nursery charges $120 per tree and $29 per tree for delivery. How many trees, including delivery, would a customer need to order for the cost at Mainer Tree Farm to be greater than Emerald Tree Nursery.
Solve and graph each given inequality.
13.15x 3 < 14x 5
14.11x 1.5 ≤ 13x 3.5
15.2y 3y 8 > 8 5y 12
16.49 3m ≥ 4m 14
17.5n 12 ≤ 3n 4
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Name:
/ Class:
/ Date:
Solve each pair of simultaneous linear equations by graphing.
18.
a. /
/ b. /
c. /
/ d. /
Determine whether the system of equations has one solution, no solution, or infinitely many solutions by graphing. If the system has one solution, name it.
19.
a. /
infinitely many solutions / b. /
one solution
c. /
one solution (–4, 4) / d. /
one solution (4, 2)
20.A line passes through (3, 4) and (6, 1). Another line passes through (–2, 4) and (4, –2). Determine if the pair of lines has no solution, one solution, or an infinite number of solutions. Explain.
21.A line passes through (0, –4) and (3, 2). Another line passes through (1, –3) and (5, 6). Determine if the pair of lines has no solution, one solution, or an infinite number of solutions. Explain.
Answer Key
2.b
3.a
4.d
5.d
6.b
7.a
8.a
9.b
10.d
11.b
12.c
13.b
14.a
15.c
16.a
17.c
18.a
19.a
20.no solution; the lines have the same slope and a different y-intercept
21.an infinite number of solutions; the lines have the same slope and the same y-intercept
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