# How do you solve #-abs(x+1)=-2#?

##### 1 Answer

The answer is:

The way to solve it is as follows.

Equal parts of an equation, left and right, can be multiplied by the same non-equal to zero multiplier getting an equivalent equation.

Let's multiply them by

Now we have to remember the definition of the *absolute value* of a number.

If the number is positive or zero, its *absolute value* equals to itself:

if

If the number is negative, its *absolute value* equals to its opposite (or, not very scientifically, minus this number)

if

Applying this to a problem at hand:

CASE 1

Looking for solutions in the area defined by an inequality

using our equation,

This value is within the area

CASE 2

Looking for solutions in the area defined by an inequality

using our equation,

This value is within the area

We can demonstrate it graphically.

Our equation is equivalent to

Let's draw a graph of a function

graph{|x+1|-2 [-10, 10, -5, 5]}

As you see, it intersects the X-axis (that is, equals to zero) at points