One Step Inequalities
x + 5 < 12
x < 7
2x + 5 < 11
x < 3
On Thursday, 435 students went on a trip to the zoo. All 8 buses were filled and 3 students had to travel in cars. How many students were in each bus ?
Equation: 8x + 3 = 435
Answer: 54 students per bus
Tyson is saving up to buy a new graphics card for his computer that costs at least $320. He has already saved $145. What is the minimum amount of additional money Tyson needs to save to afford the card?
Equation: x + 145 ≥ 320
Answer: at least $175
When multiplying or dividing on either side of an inequality, what has to happen for the inequality to flip?
The number being multiplied or divided has to be negative.
y - 8 ≥ 3
y ≥ 11
(y/3) - 4 ≥ 2
y ≥ 18
A local bookstore sells paperback books for $8 each. If Marcus buys a certain number of paperbacks and pays a flat $5 shipping fee, his total online order comes out to $45. How many paperback books did Marcus buy?
Equation: 8x + 5 = 45
Answer: 5 paperback books
An elevator has a maximum weight capacity of 2,000 pounds. A crew of movers is loading identical, heavy equipment boxes onto the elevator, and the total weight of the crew themselves is 350 pounds. If each box weighs 75 pounds, what is the maximum number of boxes they can safely load at one time?
Equation: 75x + 350 ≤ 2000
Answer: 22 boxes
When given an inequality, what order do you solve it in?
SADMEP/SADMEG
4z > 20
z > 5
-3n + 7 > 19
The sum of three consecutive even integers is 72. What is the value of the smallest of these three integers?
Equation: x+x+2+x+4 = 72
Answer: 22
A submarine is exploring the ocean floor. To avoid a thermal vent, it must stay at a depth of more than 450 feet below sea level. If the submarine descends at a constant rate of 15 feet per second, how many seconds (s) can it pass before it is safely past the vent zone?
Equation: -15s < -450
Answer: s > 30
When writing down the final answer for an expression, in what order do you put each term?
Greatest to least exponent, then alphabetically, with the constant at the end.
(w/3) ≤ -4
w ≤ -12
4p - 2.5 ≤ 9.5
p ≤ 3
Gym A charges an upfront registration fee of $50 plus $20 per month. Gym B charges no registration fee but costs $32 per month. After how many months will the total cost of both gyms be exactly the same?
Equation: 50 + 20m = 32m
Answer: m = 25/6 or 4 1/6
Kiara wants to maintain a balance of at least $500 in her bank account to avoid a monthly fee. Her current balance is $820. If she withdraws $40 each week for spending money, for how many weeks can she do this without dropping below her target balance?
Equation: 820 - 40w ≥ 500
Answer: 8 weeks
What is the correct writing of the inequality ≥ on a number line?
A solid dot/circle
-6v < 36
v > -6
-(2/3)m + 5 ≤ 1
m ≥ 6
Jordy loves candy! He knows that Jolly Ranchers are $.15 each plus $.20 for a bag to put them in. He also knows that Laffy Taffy (the big ones) are $.20 each plus $.05 for the rubber band to hold them together. If he wants to spend $5 on each type of candy, how many Jolly ranchers can he buy?
Equation: 0.15x + 0.20 =5.00
Answer: x = 32
Streaming Service Alpha offers a non-member plan where you pay $4.50 per movie rental. They also offer a VIP plan that costs $15 per month up front, but drops the rental price to $2.00 per movie. How many movies must a user rent per month for the VIP plan to be the cheaper option?
Equation: 15 + 2m < 4.50m
Answer: at least 7 movies
Always, Sometimes, or Never.
The number line for an inequality problem will have a 0 in the middle.
Sometimes