Two-Step Equations
Solve the equation
14 - 3g = 32
g = -6
The members of Starville High School's student council are planning this year's school carnival. For the raffle, they plan to order one roll of 100 golden tickets. For the carnival games, they plan to order red tickets that come in rolls of 250. Based on last year's numbers, they plan to order a total of 1,600 tickets.
Which equation can the student council use to find how many rolls of red tickets, r, they should order?
250r + 100 = 1600
Write an inequality that is represented by the number line.
<---------o------->
-5
x > 5
A school club has already raised $190. The club earns $8 for each ticket sold. The club wants to raise at least $600. Write an inequality that can be used to determine t, the number of tickets the club must sell.
190 + 8t ≥ 600
Solve the inequality
2y + 7 ≥ 11
y ≥ 2
Solve the equations
w/4 -21=-3
w=72
Scruffy Pals Pet Boxes sends pet supplies in the mail each month. Irma prepaid a 4-month subscription for her cats. She used a one-time coupon and received $8 off the total cost. Irma paid $64 in all.
Which equation can you use to find, m, the regular cost per month?
4m - 8 = 64
Write an inequality that is represented by the number line.
<--------o-------->
-8
x < -8
Emma has $75 to spend. She buys a water bottle for $21 and notebooks that cost $5 each. Write an inequality that can be used to determine n, the number of notebooks Emma can buy without spending more than $60.
21 + 5n > 75
Solve the inequality
11- 4z ≤ -1
z ≥ 3
Solve the equation
-14 = 1 + 3x
x = -5
The Glitz Jewelry Kit contains round beads in 6 different colors plus 100 star-shaped beads. There are 250 beads in all. Which equation can you use to find, r, the number of round beads in each color?
6r + 100 = 250
Write an inequality that is represented by the number line.
<-------•------->
2
x ≥ 2
An elevator can hold no more than 1,000 pounds. A delivery cart weighs 400 pounds, and each box placed on the cart weighs 58 pounds. Write an inequality that can be used to determine b, the number of boxes that can be placed on the cart.
400 + 58b ≤ 1,000
Solve the inequality
3 + 0.5b <7
b < 8
Solve the equation.
1/3 - 2d = 7
-20/6
Last summer, Emma's family rented an RV. The rental fee allowed them to use the RV for 8 days. Emma's parents paid an additional $55 for the Great Outdoors upgrade, which included a grill to use for the duration of their trip. Emma's family paid $895 in all.Which equation can you use to find the rental cost, d, of each day they used the RV?
55 + 8d = 895
Write an inequality that is represented by the number line.
<-------•------->
-1/2
x ≥ -1/2
A game shop charges $50 for each game and $5 for a carryout box. Shirley has $280 to spend. She needs to determine the most games (x) she can buy when she only puts them in one carryout box. Which equation can be used to answer this problem?
50x + 5 ≤ 280
Solve the inequality
x/-3 - 8 ≥-3
x ≤ -15
Solve the equation.
-6.3x + 7 = -5.6
x = 2
Madelyn got 3 dresses cleaned at Steamboat Dry Cleaners. When she picked up her dresses, she gave the cashier a coupon that took $2 off her total. Madelyn paid $31 in all.Which equation can you use to find the usual charge, d, for cleaning a dress?
3d - 2 = 31
Write an inequality that is represented by the number line.
<--------o-------->
17
x < 17
The temperature in the ice rink must stay below 40°F. This morning, the temperature was 120°F. The ice rink runs a cooling device that can decrease the temperature by 7.5° every hour. Which inequality shows how long it will take for the temperature to fall below 40°F?
120 - 7.5x < 40
What is the solution of the inequality z/-4 + 3 <15?
z>-48