Precalculus Examples
|8x+8||8x+8|
Step 1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
8x+8≥08x+8≥0
Step 2
Step 2.1
Subtract 88 from both sides of the inequality.
8x≥-88x≥−8
Step 2.2
Divide each term in 8x≥-88x≥−8 by 88 and simplify.
Step 2.2.1
Divide each term in 8x≥-88x≥−8 by 88.
8x8≥-888x8≥−88
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of 88.
Step 2.2.2.1.1
Cancel the common factor.
8x8≥-88
Step 2.2.2.1.2
Divide x by 1.
x≥-88
x≥-88
x≥-88
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Divide -8 by 8.
x≥-1
x≥-1
x≥-1
x≥-1
Step 3
In the piece where 8x+8 is non-negative, remove the absolute value.
8x+8
Step 4
To find the interval for the second piece, find where the inside of the absolute value is negative.
8x+8<0
Step 5
Step 5.1
Subtract 8 from both sides of the inequality.
8x<-8
Step 5.2
Divide each term in 8x<-8 by 8 and simplify.
Step 5.2.1
Divide each term in 8x<-8 by 8.
8x8<-88
Step 5.2.2
Simplify the left side.
Step 5.2.2.1
Cancel the common factor of 8.
Step 5.2.2.1.1
Cancel the common factor.
8x8<-88
Step 5.2.2.1.2
Divide x by 1.
x<-88
x<-88
x<-88
Step 5.2.3
Simplify the right side.
Step 5.2.3.1
Divide -8 by 8.
x<-1
x<-1
x<-1
x<-1
Step 6
In the piece where 8x+8 is negative, remove the absolute value and multiply by -1.
-(8x+8)
Step 7
Write as a piecewise.
{8x+8x≥-1-(8x+8)x<-1
Step 8
Step 8.1
Apply the distributive property.
{8x+8x≥-1-(8x)-1⋅8x<-1
Step 8.2
Multiply 8 by -1.
{8x+8x≥-1-8x-1⋅8x<-1
Step 8.3
Multiply -1 by 8.
{8x+8x≥-1-8x-8x<-1
{8x+8x≥-1-8x-8x<-1
