Practice Absolute Value Inequalities in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Absolute value inequalities describe values within or outside a fixed distance from a center.
means stay inside a radius; means outside it.
Showing a random 20 of 50 problems.
Example 1
mediumWrite in interval notation. Solution set of |x − 5| ≤ 2 shown as interval [3, 7]
Example 2
mediumSolve .
Example 3
mediumSolve and write it in interval notation.
Example 4
challengeSolve .
Example 5
mediumSolve and write it in interval notation.
Example 6
hardSolve .
Example 7
easySolve .
Example 8
mediumSolve . Solution set of 5 − |x| ≥ 1
Example 9
easySolve . Solution set of |x| ≤ 4
Example 10
easySolve .
Example 11
easyTrue or false: has only one solution.
Example 12
easySolve . Solution set of |x| < 6
Example 13
mediumA bolt's diameter must be within mm of mm. Express this as an absolute value inequality and find the acceptable range.
Example 14
mediumExpress or as a single absolute value inequality.
Example 15
mediumSolve . Solution set of |x − 3| + 2 < 6
Example 16
challengeFor what real does hold for ALL real ?
Example 17
challengeFor what values of does have no solution?
Example 18
easySolve .
Example 19
mediumSolve . Solution set of |x − 4| + 2 ≤ 7
Example 20
easySolve .