Question 1
Solve for x: −2x + 5 < 7
x > −1
x < −1
x > −6
x < −6
Question 2
Solve for x: 5 − (x + 5) > −2(x + 4)
x > −8
x < −8
x > −18
x < −18
Question 3
Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today. Write and solve an inequality to solve for the least amount of money she needs to deposit to avoid a fee.
524.96 − 32.50 + x ≥ 500; x ≥ $7.54
524.96 − 32.50 + x ≤ 500; x ≤ $7.54
524.96 + 32.50 − x ≥ 500; x ≥ $57.46
524.96 + 32.50 − x ≤ 500; x ≤ $57.46
Question 4
Marcie solved the following inequality, and her work is shown below:
−2(x − 5) − 12 ≤ 4 + 6(x + 3)
−2x + 10 − 12 ≤ 4 + 6x + 18
−2x − 2 ≤ 6x + 22
−8x ≤ 24
x ≤ −3
What mistake did Marcie make in solving the inequality?
She subtracted 6x from both sides when she should have added 2x.
She added 2 to both sides when she should have subtracted 22.
When dividing by −8, she did not change the ≤ to ≥.
She did not make a mistake.
Question 5
A cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddie can travel if he has $15 to spend.
$1.75 + $0.25x ≤ $15; x ≤ 53 miles
$1.75 + $0.25x ≥ $15; x ≥ 53 miles
$0.25 + $1.75x ≤ $15; x ≤ 8 miles
$0.25 + $1.75x ≥ $15; x ≥ 8 miles
Question 6
A pack of paper costs $3.75 including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write an inequality to solve for the number of packs of paper Mr. Cooper can purchase with his budget.
$3.75x ≥ $20
$3.75x ≤ $20
$20x ≤ $3.75
$20x ≥ $3.75