# 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.