Solving Equations

Solving Equations with Addition and Subtraction

You can add or subtract the same number on each side of an equation and the result is an equivalent equation . Equivalent equations have the same solution.

Example

Solve .

Solution

The number has been subtracted from x. The opposite of subtracting is adding . Add to each side of the equation. is an equivalent equation. Simplify to obtain x = 1.

Check: Is ? Yes. The solution is 1.

Solving Equations with Multiplication and Division

You can solve a multiplication or division equation by using the multiplication and division properties of equality.

Multiplication Property of Equality	For any numbers a, b, and c, if a = b, then ac = bc.
Division Property of Equality	For any numbers a, b, and c, with c 0, if a = b, then .

Example

Solve

Solution

Rewrite the mixed numbers as improper fractions.

Multiply each side by , the reciprocal of the number that is multiplied by x.

Solving Multi-Step Equations

Consecutive integers are integers in counting order, such as -3, -2, and -1.

Example

Solve .

Solution

Multiply each side by 4 to eliminate the fraction.

Next, undo the subtraction by adding 3 to each side.

2x - 3 + 3 = 36 + 3

2x = 39

Last, undo the multiplication by dividing each side by 2.