# Linear Equations

## Section 2.3

Linear Equations : Clearing Fractions and Decimals

**Example **Solve the linear equation by clearing
fractions.

1. Multiply through by the LCM of the denominators , or the LCD .

2. Solve as before .

**Example** Solve the linear equation by clearing
decimals.

21.1w + 4.6 = 10.9w + 35.2

1. Multiply through by 10, 100, 1000, etc. to clear the decimals.

2. Solve as before.

** Steps for Solving a Linear Equation in One Variable **

1. Simplify both sides of the equation.

• Clear parentheses

•Consider clearing fractions or decimals by
multiplying both sides

of the equation by a common denominator of all terms .

•Combine like terms

2. Use the addition or subtraction property of equality to
collect the vari-

able terms on one side of the equation.

3. Use the addition or subtraction property of equality to
collect the con-

stant terms on the other side of the equation.

4. Use the multiplication or division property of equality
to make the

coe cient of the variable term equal to 1.

5. Check your answer.

**Example **Solve the linear equation.

**Example** Solve the linear equation.

**Example **Solve the linear equation.

**Example** Solve the linear equation.

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