How do you solve abs(x+1)<8?

Oct 4, 2016

Solve two equations one for the positive and one for the negative.
x < 7 and x > -9

Explanation:

The absolute value is the distance form zero. These distance can be either negative or positive. Therefore it is necessary to solve for both the negative and positive values.

so the positive value would be

• ( x + 1 ) < 8 This results in

x + 1 < 8 Subtract 1 from both sides gives

x + 1 -1 < 8 -1 This gives the positive value+

x < 7

The negative value would be

-( x + 1) < 8 This results in

-x - 1 < 8 Add +1 to both sides gives

• x -1 + 1 < 8 + 1 this gives

-x < 9 solve by dividing everything by -1

$- \frac{x}{-} 1 < \frac{9}{-} 1$ This gives

x > -9