Algebra Examples

Graph |2x+2|-7<=-5
Step 1
Write as a piecewise.
Tap for more steps...
Step 1.1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Step 1.2
Solve the inequality.
Tap for more steps...
Step 1.2.1
Subtract from both sides of the inequality.
Step 1.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 1.2.2.1
Divide each term in by .
Step 1.2.2.2
Simplify the left side.
Tap for more steps...
Step 1.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 1.2.2.2.1.1
Cancel the common factor.
Step 1.2.2.2.1.2
Divide by .
Step 1.2.2.3
Simplify the right side.
Tap for more steps...
Step 1.2.2.3.1
Divide by .
Step 1.3
In the piece where is non-negative, remove the absolute value.
Step 1.4
To find the interval for the second piece, find where the inside of the absolute value is negative.
Step 1.5
Solve the inequality.
Tap for more steps...
Step 1.5.1
Subtract from both sides of the inequality.
Step 1.5.2
Divide each term in by and simplify.
Tap for more steps...
Step 1.5.2.1
Divide each term in by .
Step 1.5.2.2
Simplify the left side.
Tap for more steps...
Step 1.5.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 1.5.2.2.1.1
Cancel the common factor.
Step 1.5.2.2.1.2
Divide by .
Step 1.5.2.3
Simplify the right side.
Tap for more steps...
Step 1.5.2.3.1
Divide by .
Step 1.6
In the piece where is negative, remove the absolute value and multiply by .
Step 1.7
Write as a piecewise.
Step 1.8
Subtract from .
Step 1.9
Simplify .
Tap for more steps...
Step 1.9.1
Simplify each term.
Tap for more steps...
Step 1.9.1.1
Apply the distributive property.
Step 1.9.1.2
Multiply by .
Step 1.9.1.3
Multiply by .
Step 1.9.2
Subtract from .
Step 2
Solve when .
Tap for more steps...
Step 2.1
Solve for .
Tap for more steps...
Step 2.1.1
Move all terms not containing to the right side of the inequality.
Tap for more steps...
Step 2.1.1.1
Add to both sides of the inequality.
Step 2.1.1.2
Add and .
Step 2.1.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.1.2.1
Divide each term in by .
Step 2.1.2.2
Simplify the left side.
Tap for more steps...
Step 2.1.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.1.2.2.1.1
Cancel the common factor.
Step 2.1.2.2.1.2
Divide by .
Step 2.1.2.3
Simplify the right side.
Tap for more steps...
Step 2.1.2.3.1
Divide by .
Step 2.2
Find the intersection of and .
Step 3
Solve when .
Tap for more steps...
Step 3.1
Solve for .
Tap for more steps...
Step 3.1.1
Move all terms not containing to the right side of the inequality.
Tap for more steps...
Step 3.1.1.1
Add to both sides of the inequality.
Step 3.1.1.2
Add and .
Step 3.1.2
Divide each term in by and simplify.
Tap for more steps...
Step 3.1.2.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Step 3.1.2.2
Simplify the left side.
Tap for more steps...
Step 3.1.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.1.2.2.1.1
Cancel the common factor.
Step 3.1.2.2.1.2
Divide by .
Step 3.1.2.3
Simplify the right side.
Tap for more steps...
Step 3.1.2.3.1
Divide by .
Step 3.2
Find the intersection of and .
Step 4
Find the union of the solutions.
Step 5