Verified answer

|x| < 7

means:

-7 < x < 7

|2 - 3x| ≤ 4

becomes:

-4 ≤ 2 - 3x ≤ 4

subtract 2 from each part:

-6 ≤ -3x ≤ 2

divide through by -3, reversing inequality:

2 ≥ x ≥ -2/3

turn in around:

-2/3 ≤ x ≤ 2

that's it! ;)

|absolute values| always have two possible outputs

The absolute value bars ask how far a number is from 0 without regard to direction

so it could be left (negative) or right (positive).

|x | <7

gives

x > -7 and x< 7 or to make it a compound inequality -7< x < 7

(between)

|2 - 3x| ≤ 4

gives

2 - 3x ≥ - 4 and 2 - 3x ≤ 4

- 3x ≥ -6................-3x ≤ 2.......If you multiply or divide by a negative

x ≤ 2........................x ≥ -2/3....you must switch the direction of the inequality