Two-Step Equations
Find the value of m:
4m−6=184m
m=6
Jordan needs $124.50 for a sports camp. He already has $22.50 and can earn the rest by working 8 hours at his job. Write an equation to find h, Jordan’s hourly earnings.
22.50+8h=124.50
Solve for x.
3(5x+7)=22
x=3
2+25h<12
h<4
A stadium can hold 2,500 people. There are currently 1,800 people inside, and 10 more people enter every minute.
Write an inequality to represent the situation, where m is the number of minutes, to ensure the stadium does not exceed its capacity.
1800+10m≤2500
Find the Value of n.
3.50+4.25n=52.75
Round to the nearest tenth.
n=11.6
Emma buys pencils and notebooks for her classroom. The pencils cost $3.50 and the notebooks cost $4.25 each. Emma spends a total of $52.75. Write an equation to represent the situation. Round to the nearest tenth.
3.50+4.25n=52.75
Distribute the terms.
-1(2x+5)
-2x-6
Solve for m.
1800+10m≤2500
m≤70
Solve and graph the solution to the inequality:
-5x-8>2
x<-2
Graph on your number line provided. It should be an open circle on -2 moving to the left of -2.
Solve for b.
4b+6=30
b=6
Lauren buys Takis for a party. Each bag of Takis costs $3.50. She also pays a $5 entrance fee for the store. Lauren spends a total of $24.50. Write a two-step equation to represent the situation.
3.50b+5=24.50
Distribute the terms.
3(22x-1)
66x-3
Solve for x.
−3x+7≤10
x≥−1
Graph the solution x≤−1 on your paper.
Closed circle on -1 with line going to the left.
Solve for x.
2/3x+5=11
x=9
Ms. Schafer buys Takis for her class party. Each bag of Takis costs $4, and she also pays a $6 delivery fee from Door Dash. If Ms. Schafer spends a total of $30, write a two-step equation to find b, the number of bags of Takis she bought.
4b+6=30
Distribute the terms:
2(3x-7.5)
6x-15
2x−7<9
x<8
Ms. Schafer has 2 desk geese in her classroom. Each goose eats 1/2 cup of birdseed per day. She wants to make sure the geese eat less than 5 cups of birdseed total in one week.
Write an inequality to find the number of days, d, the geese can be fed without exceeding 5 cups.
1d<5
or
d<5
A student solved the equation:
−3(y+5)=24
using the following steps:
−3y+5=24
−3y=19
-3y = 19
y=19/3
Did the student solve the equation correctly? If not, explain the error(s) and find the correct solution.
−3(y+5)=24
-3𝑦+5=24(Student distributed incorrectly)
−3𝑦=19
𝑦=−19/3
Correct Answer: y=−13
Ms. Schafer buys 3 cups of birdseed per day for her 2 desk geese and Biggie Cheese. She also buys an extra 6 cups of birdseed to have on hand. If she has 24 cups total, write a two-step equation to find d, the number of days the birdseed will last.
3d+6=24
Distribute the terms.
.5(x-3)
.5x-1.5
Solve for x.
−4x+6≥10
x≤−1
Ms. Schafer’s 2 desk geese each drink 3/4 cup of water per day. She has a total of 10 cups of water available.
Write a two-step inequality to find the number of days, ddd, the geese can drink without running out of water.
3/2⋅d≤10