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.