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 59 problems.
Example 1
easy
Solve: −x<3.Solution set of −x < 3 after flipping; open circle because strictly greater than
Example 2
medium
Maya saves $8 per week. She already has $20. For how many weeks w will her total be at least $60?
Example 3
medium
Solve the compound inequality 1≤3x−2<10.
Example 4
hard
For what values of k does the inequality x2+kx+4>0 hold for all real x?
Example 5
easy
Is x=4 a solution to x>4?
Example 6
medium
The temperature is 0∘ now and drops 3 degrees every hour, so after h hours it is −3h degrees. After how many whole hours will the temperature first be below −12∘? Enter the number of hours.
Example 7
easy
Translate to an inequality: 'a number n is at least −3'.
Example 8
easy
Solve: x+4<9.Solution set of x + 4 < 9
Example 9
medium
Write the inequality whose solution is x≤−1 or x≥4 as the complement of a single compound inequality.
Example 10
easy
Solve: 2x<10.Solution set of 2x < 10; dividing by positive 2 keeps the direction
Example 11
easy
Write 'all numbers greater than −1' as an inequality.
Example 12
easy
Fill the blank with a number so that the solution is x>4: x+__>9.
Example 13
medium
Solve 3(x−2)≤9.
Example 14
easy
Graph the solution to x≤2 on a number line — open or closed circle at 2?x ≤ 2 graphed: closed circle at 2 because ≤ includes the endpoint
Example 15
easy
Solve x+7≤12.Solution set of x + 7 ≤ 12
Example 16
medium
Solve: −3x≥2.
Example 17
medium
Express −3≤x<5 in interval notation.
Example 18
easy
Solve: x−3≥2.Solution set of x − 3 ≥ 2; closed circle shows 5 is included
Example 19
challenge
Find all x with ∣x−3∣<5 and express in interval notation.Solution set of |x − 3| < 5; both endpoints excluded
Example 20
medium
Fill the blank with a number so that the solution is x≤3: −2x≥__.