Verified answer

To get started, get the absolute value on one side and everything else on the other. To do this, subtract 3 from each side in the inequality |5 – 3x| + 3 ≤ 7.

Now we have

|5 – 3x| ≤ 4

This means that 5 – 3x ≤ 4 and 5 – 3x ≥ - 4

Solve both inequalities.

5 – 3x ≤ 4

Subtract 5 from each side

-3x ≤ -1

Divide each side by -3

x ≥ 1/3 (notice that ≤ became ≥ which happens when dividing by a negative number)

5 – 3x ≥ - 4

Subtract 5 from each side

-3x ≥ - 9

Divide each side by -3

x ≤ 3 (notice that the inquality flipped again because we divided by a negative)

So the solutions are x ≥ 1/3 and x ≤ 3 which is the same as 1/3 ≤ x ≤ 3

|5-3x|<4

5-3x<4 -3x<-1 x<1/3

5-3x>-4 -3x>-9 x>3

The first solution is right