Solving One Step Inequalities
Solve the inequality
6.9 < x−2.3
x > 9.2
Solve the inequality:
6.5x − 11.3 ≤ 8.2
x ≤ 3
Drew practices piano at least 45 minutes per day. He has already practiced 18.5 minutes today.
x + 18.5 ≥ 45
Miles is selling cookies at his school for $2 per box. He has already sold $18 worth of cookies. He needs to sell a minimum of $100 worth of boxes to earn a cool prize from his school. Write and solve an inequality that shows how many more boxes Miles needs to sell to meet his goal.
2x +18 ≤ 100
x ≤ 41
3x > 12
x > 4
Solve the inequality
x + 8 ≥ 14
x ≥ 6
Solve the inequality:
−2.45x + 3.2 < −6.6
x > 4
Paul is making picture frames. He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.
Write an inequality that can be used to determine how much material, x, Paul should buy.
x/24.5 ≥ 8
A rental company charges $15 plus $4 per hour to rent a bicycle. Margie wants to spend no more than $27 for her rental.
Write an inequality that can be used to determine how many hours, x, Margie can rent the bicycle and spend no more than $27.
15 + 4x ≤ 27
1.) Solve: 2 ≤ 0.25 x
2.) Graph the solution on a number line
1.) x ≥ 8
2.) Teacher Graded
Solve the inequality
x − 3/4 < 1/2
x < 1 1/4
Solve the inequality:
−4 ≤ 4x + 8
x ≥ −3
William is 3 feet 1 inch tall and would like to ride a roller coaster. Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller William must be.
x + 37 ≥ 42
Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting.
Write an inequality that can be used to determine how many hours, x, Matilda will need to babysit to buy the dress.
9x + 40 ≥ 112
x/3 < 5
x < 15
Solve the inequality
−6x > 66
x < −11
Solve the inequality:
1/2x −1/4 < 5/8
x < 1 3/4
After a number of months, a bank balance was –$46.83. Each month, the bank charges a $5.95 fee for having a negative balance. Write an inequality to determine at most how many months the fee was charged. Let x be how many months the fee was charged.
−5.95x > −46.83
Douglas bought a $20 game card at a game center. The go-karts cost $3.50 each time you race. He wants to have at least $7.75 left on his card to play arcade games. Write an inequality to determine how many times Douglas can race the go-karts.
20 − 3.5x ≥ 7.75
−2.4 ≥ x/5
x ≤ −12
In an online game, you receive –3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most –27. When the character slips, it takes 2 seconds for him to resume the race. Write an inequality to find the least number of bananas your character slipped on. Let x be the number of bananas your character slipped on.
−3x ≤ −27
Solve the inequality:
−2 (x+2) < x + 8
x > −4
Greg's grandmother is knitting scarves for charity. The table shows the number of yards needed for different types of scarves.
Bulky: 150 yards required
Light: 250 yards required
Medium: 200 yards required
She plans to make bulky scarves and has no more than 2,250 yards of yarn. Write the inequality to solve. If the charity plans to sell the scarves for $24.50, how much money will the charity make?
150x ≤ 2,250
$367.50
Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Write and solve an inequality to determine how many times Robin can go to the movies this month. Then interpret the solution.
40 - 5x ≤ 12.50
Ben needs to buy an equal number of sunglasses and beach balls to place in gift bags. Each pair of sunglasses costs $4 and each beach ball costs $2.50. If he has $45 to spend on the sunglasses and beach balls, then the inequality 4x + 2.5x ≤ 45 can be used to find the number of each item he can buy. How much money will he have left after buying the greatest number of sunglasses and beach balls?
$6