# Algebra Examples

Move to the left side of the equation by subtracting it from both sides.

Convert the inequality to an equation.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Set the factor equal to .

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

Set the factor equal to .

Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.

The equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .

Defined on all real numbers

Use each root to create test intervals.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

Simplify.

Simplify each term.

Raise to the power of to get .

Multiply by to get .

Simplify by subtracting numbers.

Subtract from to get .

Subtract from to get .

The left side is greater than the right side , which means the given statement is false.

False

False

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

Simplify.

Simplify each term.

Raise to the power of to get .

Multiply by to get .

Simplify by subtracting numbers.

Subtract from to get .

Subtract from to get .

The left side is less than the right side , which means the given statement is true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

Simplify.

Simplify each term.

Remove parentheses around .

Raise to the power of to get .

Multiply by to get .

Simplify by adding and subtracting.

Add and to get .

Subtract from to get .

The left side is greater than the right side , which means the given statement is false.

False

False

Compare the intervals to determine which ones satisfy the original inequality.

False

True

False

False

True

False

The solution consists of all of the true intervals.