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 Number of inequalities to solve: 23456789
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## 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.

 Addition Property of Equality For any numbers a, b, and c, if a = b, then a + c = b + c. Subtraction Property of Equality For any numbers a, b, and c, if a = b, then a - c = b - c. Solving Equations To solve an equation means to get the variable (with a coefficient of 1) by itself on one side of the equation. You can do this by undoing what has been done to the variable, using the properties of equality.

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

 Solving Multi-Step Equations Work backward to isolate the variable and solve the equation. Use subtraction to undo addition, and use addition to undo subtraction. Use multiplication to undo division, and use division to undo multiplication.

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.