Answer :

The solution for the given absolute value inequality is -1/3 ≤ x ≤ 5/3.

How to solve absolute value inequalities?

  • 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.

Calculation:

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:

https://brainly.com/question/15977483

#SPJ9

Other Questions