Question

Solve for x.
-12< -3x - 15 < 36
Enter your answer, as one inequality, in the box.

Answer 1

Explanation:

-12 < -3x - 15 <= 36 | add 15 everywhere

3 < -3x <= 51 | divide by 3 everywhere

1 < -x <= 17 | multiply by -1 everywhere

-1 > x >= -17

or

-17 <= x < -1

remember that with every multiplication or division of a negative number the orientation of the inequality signs flip.

the same happens, of course, when we exchange the upper and lower limits from left to right and right to left, so that the smaller number is on the left, and the larger number on the right (yes, -1 is larger than -17).