3|x-2|>15

⚑ Flag

The key with absolute value is to always follow the 4 steps in exact order. 1. Isolate the absolute value. In this case, there is a 3 outside the absolute value. We can't distribute into the bars, so we must divide by 3 on both sides to simply remove it. |x-2| > 5 2. Check for solutions. < -# means No solutions. > -# means All real numbers. >or< +# means 2 solutions. You may be done at this point, but if you need to keep going (which we do because our absolute value is > +#)... 3. Split into 2 equations. Because the absolute value of a negative number will be the same as its positive counterpart, we have 2 options. x - 2 > 5  or  x - 2 < -5 (Notice here is where we remove the absolute value bars.) 4. Solve the 2 inequalities. x - 2 > 5  or  x - 2 < -5 Add 2 to both sides x > 7  or  x < -3. Graphed on a number line, it would be an open circle on -3 shaded to the left and an open circle on 7 shaded to the right.