Mathematical statements that compare two expressions using symbols like <, >, ≤, or ≥, indicating that one quantity is less than, greater than, or not equal to another. Unlike equations, inequalities describe a range of possible solutions.
Instead of 'equals exactly,' it's 'at least,' 'at most,' or 'greater/less than.'
Showing a random 20 of 50 problems.
Example 1
easy
Solve: x−3≥2.Solution set of x − 3 ≥ 2; closed circle shows 5 is included
Example 2
medium
Solve: 5−3x<2x−10.
Example 3
easy
Solve: x+4<9.Solution set of x + 4 < 9
Example 4
challenge
For what values of k does kx>6 give x<6/k?
Example 5
hard
Solve 4−2x≥10.Solution set of 4 − 2x ≥ 10 graphed on the number line
Example 6
medium
How many integers satisfy −4<x≤5?
Example 7
easy
Solve: −x<3.Solution set of −x < 3 after flipping; open circle because strictly greater than
Example 8
easy
Write the inequality represented by 'an open circle at 4 with shading to the right'.
Example 9
easy
Translate to an inequality: 'a number n is at least −3'.
Example 10
medium
Solve: −2x+5≤1.Solution set of −2x + 5 ≤ 1; flip when dividing by −2
Example 11
easy
Solve: 2x<10.Solution set of 2x < 10; dividing by positive 2 keeps the direction
Example 12
easy
Solve −4x>12 and explain the sign flip.Solution set of −4x > 12; dividing by −4 flips the inequality
Example 13
hard
Solve x+2x−1≥0.
Example 14
medium
Express −3≤x<5 in interval notation.
Example 15
medium
Maya saves $8 per week. She already has $20. For how many weeks w will her total be at least $60?
Example 16
medium
A car rental costs $25 per day plus $0.20 per mile. With $100 for a 2-day rental, how many miles m can you drive?
Example 17
easy
Solve 4x<3.Solution set of x/4 < 3
Example 18
medium
Solve: 2(x−1)>x+3.
Example 19
medium
Solve the compound inequality: −3<2x−1≤5.Solution set of −3 < 2x − 1 ≤ 5; left endpoint excluded, right included
Example 20
easy
Solve 2x+5>11.Solution set of 2x + 5 > 11 graphed on the number line