# Algebra Examples

Find the Inverse 1/4x-7
Step 1
Interchange the variables.
Step 2
Solve for .
Step 2.1
Rewrite the equation as .
Step 2.2
Combine and .
Step 2.3
Add to both sides of the equation.
Step 2.4
Multiply both sides of the equation by .
Step 2.5
Simplify both sides of the equation.
Step 2.5.1
Simplify the left side.
Step 2.5.1.1
Cancel the common factor of .
Step 2.5.1.1.1
Cancel the common factor.
Step 2.5.1.1.2
Rewrite the expression.
Step 2.5.2
Simplify the right side.
Step 2.5.2.1
Simplify .
Step 2.5.2.1.1
Apply the distributive property.
Step 2.5.2.1.2
Multiply by .
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Simplify each term.
Step 4.2.3.1
Combine and .
Step 4.2.3.2
Apply the distributive property.
Step 4.2.3.3
Cancel the common factor of .
Step 4.2.3.3.1
Cancel the common factor.
Step 4.2.3.3.2
Rewrite the expression.
Step 4.2.3.4
Multiply by .
Step 4.2.4
Combine the opposite terms in .
Step 4.2.4.1
Step 4.2.4.2
Step 4.3
Evaluate .
Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Simplify each term.
Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Cancel the common factor of .
Step 4.3.3.2.1
Factor out of .
Step 4.3.3.2.2
Cancel the common factor.
Step 4.3.3.2.3
Rewrite the expression.
Step 4.3.3.3
Cancel the common factor of .
Step 4.3.3.3.1
Factor out of .
Step 4.3.3.3.2
Cancel the common factor.
Step 4.3.3.3.3
Rewrite the expression.
Step 4.3.4
Combine the opposite terms in .
Step 4.3.4.1
Subtract from .
Step 4.3.4.2