One Step Inequalities
Solve: d−17 ≤ 34
d ≤ 51
Solve: 3d + 7 > −2
d > -3
Graph the compound inequality for x<5 or x>11.
Open circles shading outward.
Solve: |x+5| ≤ 4
-9 ≤ x ≤ -1
A group of friends plan to go to a concert. They should bring money for tickets, meals and souvenirs. They are told to bring at least $50 but no more than $125. Write a compound inequality that represents the amounts of money, m, each person can bring.
50 ≤ x ≤ 125 dollars
Solve: d + 12 ≤ −28
d ≤ −40
Solve: 4x − 5 ≤ 11
x ≤ 4
Solve: -3 ≤ x + 4 < 10
-7 ≤ x < 6
Solve: |x| ≤ 4
-4 ≤ x ≤ 4
A poll shows that 75% of the voters say they plan to vote for an issue. The margin of error is ±10 percentage points.
a) Write an absolute value inequality that represents the range of percents of voters, p, who plan to vote for the issue.
b) Solve the absolute value inequality that represents the range of percents of voters, p, who plan to vote for the issue.
a.) | p - 75 | ≤ 10
b.) 65% ≤ p ≤ 85%
Solve: −7d > −49
d<7
Solve: 4x − 3 > 12
x > 15/4
Solve: -2 < -3x + 7 ≤ 4
3 > x ≥ 1
(1 ≤ x < 3)
Solve: |x+7| > 4
x > -3 or x < -11?
You are building a rock wall for a flower bed along your 20-foot long driveway. You want the wall to be one-half of the length of the driveway with an absolute deviation of at most 5 feet.
a) Write an absolute value inequality that represents the possible lengths, w, of the wall.
b) Solve the absolute value inequality that represents the possible lengths, w, of the wall.
a.) |w-15|≤ 5
b.) 10 ≤ w ≤ 20 ft.
Solve: −¾d ≥ −525
d ≤ 700
Solve: 3x > 5x + 12
x < -6
Solve: -2 ≤ 5-x ≤ 2
7 ≥ x ≥ 3
(3 ≤ x ≤ 7)
Solve: |x+5| - 11 ≤ 4
-20 ≤ x ≤ 10
Write and graph an inequality for:
A number m is fewer than 9 or at least 12.
m < 9 or m ≥ 12
Solve: d - 12 < -14
d < -2
Solve: 3x − 5 > 2x + 10
x > 15
Solve: 3x - 1 < -7 or 4x + 1 > 9
x<-2 or x>2?
Solve: |x-2|+ 10 > 5
All real numbers.
Write and graph:
A number k is more than 6 and no more than 8.
k > 6 and k ≤ 8