The solution for the given absolute value inequality is -1/3 ≤ x ≤ 5/3.
<h3>How to solve absolute value inequalities?</h3>
- The solution for the absolute value inequality of the form |x| ≤ p is -p ≤ x ≤ p.
- The solution for the absolute value inequality of the form |x| ≥ p is x ≤ -p or x ≥ p.
<h3>Calculation:</h3>
The given absolute value inequality is
|3x - 2| + 4 ≤ 7
Subtracting 4 from both sides,
⇒ |3x - 2| + 4 - 4 ≤ 7 - 4
⇒ |3x - 2| ≤ 3
This is in the form of |x| ≤ p; then it is replaced with the compound inequality -p ≤ x ≤ p
⇒ -3 ≤ 3x - 2 ≤ 3
Adding 2,
-3 + 2 ≤ 3x - 2 + 2 ≤ 3 + 2
⇒ -1 ≤ 3x ≤ 5
Dividing by 3,
-1/3 ≤ 3x/3 ≤ 5/3
⇒ -1/3 ≤ x ≤ 5/3
Therefore, the solution for the given absolute value inequality is -1/3 ≤ x ≤ 5/3.
Learn more about absolute value inequalities here:
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