One-Step Inequalities
Solve and graph:
x + 3 < 8
What is x < 5?
Graph: Open circle on 5, shaded to the left.
3 - x ≤ 15
What is x ≥ -12?
−2(x + 11) < −18
What is x > -2?
7y - 6 > 9y
What is y < -3 or -3 > y?
An equivalent ratio of 5:3
What is 10:6, 15:9, 20:12, etc.?
Solve and graph:
2x > 8
What is x>4?
Graph: Open circle on 4, shaded to the right.
−2x + 3 < -3
What is x>3?
36 < 4(20 + x)
What is x > -11 or -11 < x?
-5n - 6 ≥ -2n + 3
What is n ≤ -3 or -3 ≥ n?
This ratio is not equivalent to the others.
A) 2:9
B) 4:27
C) 8:36
D) 6:27
What is B) 4:27?
Solve and graph:
x + 6 ≤ -15
What is x ≤ -21?
Graph: Closed circle on -21, shaded to the left.
(2x)/3 ≥ 12
What is x≥18?
9 > 2m - 2 - 3m
What is m > -11 or -11 < m?
-1 - 6x - 6 > -2x -11 - 4x
Does the inequality have infinite solutions?
Solve the proportion using equivalent fractions:
(2/3) = (x/18)
What is x=12?
Solve and graph:
-3 + x ≥ 7
What is x≥10?
Graph: Closed circle on 10, shaded to the right.
3x - 7 > 17
What is x>8?
(2x/3) - 7 ≤ 11
What is x≤27?
-8x - 16 + 10x > -5x + 7x
Does the inequality have no solution?
This rate represents the following scenario: Mr. Barnes drives 120 miles in 4 hours.
What is 120 (miles): 4 (hours); 60 (miles): 2 (hours); 30 (miles): 1 (hour)?
Solve and graph:
(x/3) ≥ 12
What is x≥36?
Graph: Closed circle on 36, shaded to the right.
5 - (x/3) < 12
What is x > -21?
167 ≥ 6 + 7(2 - 7r)
What is r ≥ -3 or -3 ≤ r?
-5n + 6 ≤ -7(5n - 6) + 30n
Does the inequality have infinite solutions?
Solve using cross-multiplication:
(4 - x)/3 = (x + 12)/6
What is x = -12/9 OR x = -4/3 OR x = -1.3 (3 repeating)?