Word Problems
You need to earn at least $75. You earn $6.00 for each hour you work. Write and solve an inequality that represents the number of hours h that you need to work.
22.
6x ≥ 75
x ≥ 12.50
4p < 6p + 12
9.
p > -6
x + 5 ≤ -2
<—————————————>
6.
x ≤ -7
<~~~~⚫️-------->
-7
Write the sentence as an inequality.
The product of a number n and 2 is no less than 14
1.
2n ≥ 14
-8(x - 4) -3 ≤ 5
Interval Notation:
<—————————->
1.
x ≥ 3
[3, ∞)
<——————⚫️~~~~~>
3
You need at least 150 cups of lemonade but less than 225 cups of lemonade for a picnic. Each batch of lemonade makes 25 cups of lemonade. Write and solve an inequality that represents the number of batches b you need to make.
23.
150 < 25b < 225
6 < b < 9
2k > 2k + 4
8.
no solution
4q > -28
<—————————————>
7.
4q > -28
<——————⚪️~~~~~~~~>
-7
Write the sentence as an inequality.
The speed “s“ on a highway is at most 60 miles per hour.
2.
s ≤ 60
5x + 8 ≤ 1/2 (6x - 4)
<————————————>
Interval Notation:
2.
x ≤ -5
(-∞, -5]
<~~~~~~⚫️———>
-5
You have a goal to practice the piano for an average of at least 50 minutes per day for one week. The first six days you practice a total of 245 minutes. Write and solve an inequality that represents the number of minutes m you need to practice on the seventh day.
24.
245 + m ≥ 50(7)
m ≥ 105
2.5w - 5 < 2w + 5
10.
w < 20
5 + 2y < 8 or 5y > 3y + 7
<————————————->
14.
y < 3/2 or y > 7/2
<~~~~~⚪️——-⚪️~~~~~~>
3/2 7/2
Write the sentence as an inequality.
The length “r” of a rope should be at least 28 inches.
3.
r ≥ 28
-x - 10 ≥ -3 or 5x - 2 > -27
<—————————————>
Interval Notation:
6.
x ≤ -7 or x > -5
(-∞,-7] or (-5, ∞)
<~~~⚫️——⚪️~~~~~>
-7 -5
The cost to rent a construction crane is $1500 per day plus $250 per hour of use. Write and solve an inequality that can be used to determine the maximum number of hours h the crane can be used if the rental cost for the one day will not exceed $5000.
25.
1500 +250h ≤ 5000
h ≤ 14
5 (p - 1) > 6p - 7
11.
p < 2
7 < 12 + c < 13
<-————————————->
15.
-5 < c < 1
<———-⚪️~~~~~⚪️———->
Write and graph a compound inequality that represents the numbers that are NOT solutions of the inequality represented by the graph shown.
<——-⚫️~~~~~~⚪️———>
0 5
20.
x < 0 or x ≥ 5
<~~~~⚪️———⚫️~~~~~>
0 5
x - 2 < -11 or -3x ≤ -18
<————————————->
Interval Notation:
5.
x < -9 or x ≥ 6
(-∞, -9) or [6, ∞)
<~~~⚪️———⚫️~~~~>
-9 6
The costume store Spirit is having a Halloween sale. The store has a rule that customers can only purchase costumes that cost between $30 and $80. Let's represent the cost of a costume as "c" dollars. Write a compound inequality that represents the cost, c, of a costume that a customer can purchase from the store.
30 ≤ c ≤ 80.
5 - 2x < 4 - 2x + 3
13.
Always true
5 < 7
-3p +1 ≤ -11 or -0.5p > 12
<—————————————>
16.
p < -24 or p ≥ 4
<~~~~~⚪️———⚫️~~~~~>
-24 4
Write and graph a compound inequality that represents the numbers that are NOT solutions of the inequality represented by the graph shown.
<~~~~⚪️———⚪️~~~~>
1 3
21.
1 ≤ x ≤ 3
<——--⚫️~~~~~⚫️———>
7 - (5 - 4x) < 2 (3x + 8)
<————————————->
Interval Notation:
3.
x > -7
(-7,∞)
<——⚪️~~~~~~>
-7