Question

|x+5|>12 graph the solution and write in interval notation

Answer 1

Answer: Interval notation:
`(-\infty,-17)\cup(7,\infty)`

Graph in picture

Explanation:

This is an absolute value inequality, so start by writing 2 inequalities:

x+5 > 12

x+5 > -12

For the first, x+5 > 12

Subtract 5 from both sides: x + 5 - 5 > 12 - 5

x > 7 is the solution to the first absolute value equation.

Then, for x+5 > -12,

Subtract 5 from both sides: x+5 - 5 > - 12 - 5

x > - 17 is the solution to the second absolute value equation.

To graph this, use vertical dotted lines crossing the x-axis at (7,0) and (-17,0). The shaded region will be on the outside of both lines as the left side goes from -17 to negative infinity and the right side goes from 7 to positive infinity.

In interval notation, this is: (-inf, -17) U (7, inf).
`(-\infty,-17)\cup(7,\infty)`