Solve the inequality. Write the solution in interval notation.

Question

|2 - 3x| <= 5

Select the correct choice below, and fill in the answer box if necessary.

OA. The solution set is ___ (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
B. There is no solution.

Answer 1

To solve the inequality |2 - 3x| <= 5, we can break it down into two separate inequalities:

1) 2 - 3x <= 5
2) -(2 - 3x) <= 5

For inequality 1, we subtract 2 from both sides:
-3x <= 3

Dividing both sides by -3 (and reversing the inequality since we are dividing by a negative number) gives:
x >= -1

For inequality 2, we distribute the negative sign and simplify:
-2 + 3x <= 5

Adding 2 to both sides gives:
3x <= 7

Dividing both sides by 3 gives:
x <= 7/3

Putting the solution to both inequalities together, we have:
x >= -1 and x <= 7/3

In interval notation, this can be written as:
[-1, 7/3]