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Try to rewrite this inequality as a compound inequality.
- 36≤ x≤ 28
Now, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number less than or equal to 32 away from the midpoint in the positive direction and any number less than or equal to 32 away from the midpoint in the negative direction. Absolute Value Inequality:& |x+4|≤ 32 Compound Inequality:& - 32≤ x+4 ≤ 32 We can split this compound inequality into two cases, one where x+4 is greater than or equal to - 32 and one where x+4 is less than or equal to 32. x+4≥- 32 and x+4≤ 32 Let's isolate x in both of these cases before graphing the solution set.
The solution to this type of compound inequality is the overlap of the solution sets. Let's recombine our cases back into one compound inequality. First Solution Set:& - 36≤ x Second Solution Set:& x≤ 28 Intersecting Solution Set:& - 36≤ x≤ 28