Question

solve the inequality |2x+12|>38

Answer 1

Using the definition of absolute value, the solution is all x for which 2x + 12 < -38 or 2x + 12 > 38. Solve those two inequalities to find all solutions. 2x + 12 < -38 implies that x < (-38 - 12) / 2. 2x + 12 > 38 implies x > (38 - 12) / 2.

Answer 2

For the absolute value function, I find it helpful to visual the real number line and remember that absolute value just tells how far the number is to the right or left of 0. The inequality says that the number 2x+12 has to be further than 38 from 0 to left or right. So you just find all x which makes that happen.