Inequalities (Medium)
Solve and graph on a number line:
5x - 4 < 3x + 6
x < 5
Solve and graph on a number line:
4(x + 2)≥ -3x - 6
x ≥ -2
Solve and graph on a number line:
-3 < 2x + 1 < 9
−2 < x < 4
Solve and graph on a number line:
6 − 7x ≥ −6x and − 2x ≤ −x + 6
−6 ≤ x ≤ 6
Ms. Haney started the year with $1000 in her bank account. She spends $100 per month on bills. She wants to save at least $300 in her account.
How many months can Ms. Haney keep paying bills?
Write an inequality, solve, and graph on a number line.
1000 - 100x ≥ 300
x ≤ 7 months
Solve and graph on a number line:
3x + 8 ≤ -4x + 1
x ≤ -1
Solve and graph on a number line:
−3(x − 3) − 6 ≥ 12
x ≤ −3
Solve and graph on a number line:
4 < 6 + 2x < 24
−1 < x < 9
Solve and graph on a number line:
9x < 8x + 2 or 10x ≥ 6x + 5
x < 2 or x ≥ 5/4
Daniel has a total of $25 to spend at the fair. If the initial cost for the fair is $4 and the rides cost $1.50 each, what is the most number of rides Daniel can go on?
Write an inequality, solve, and graph on a number line.
4 + 1.50 ≤ 25
x ≤ 14 rides
Solve and graph on a number line:
3(x+2) > 5x
3 > x
Solve and graph on a number line:
−17 + 8x ≥ 5(7x + 2)
x ≤ −1
Solve and graph on a number line:
7x − 3 ≥ 46 or 7 + 9x < −2
x ≥ 7 or x < −1
Solve and graph on a number line:
5x − 10 < 10x + 5 or 4x − 7 > 5x + 6
x > −3 or x < −13
Allison practices her violin for at least 13 hours per week. She practices for 2 hours each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to at least reach her goal?
Write an equality, solve, and graph on a number line.
2x + 3 ≥ 13
x ≥ 5 sessions
Solve and graph on a number line.
-3x - 8 ≤ -2x - 5
-3 ≤ x
Solve and graph on a number line:
7(1 + x) < −33 −x
x < −5
Solve and graph on a number line:
5x − 4 > −9 or 7 + 6x < −53
x > −1 or x < −10
Solve and graph on a number line:
-3 < -3(x+1) - 4x + 7 < 13
-9/7 < x < 1
A taxi charges a starting rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Write an inequality, solve, and graph on a number line.
1.75 + 0.65x ≤ 10
x ≤ 12.7 miles
Solve and graph on a number line:
-9x + 14 < 27x - 15
29/36 < x
Solve and graph on a number line:
−4x + 4(3 − 5x) ≤ −6(6x − 8)
x ≤ 3
Solve and graph on a number line:
-3 < -3(x + 5) < 6
Solve and graph on a number line:
8x + 7 ≤ 4x + 7 or 5 + 3x < −8 + 2x
x ≤ 0
The seventh grade class is putting on a talent show to raise money. The initial cost is $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000?
Write an inequality, solve, and graph on a number line.
15x - 700 ≥ 1000
x ≥ 114 tickets