1. Solving Equations Containing Fractions
Chapter 1 / Whole Numbers and Introduction to Algebra
Section 4.8
Solving Equations Containing Fractions

2. Addition Property of Equality
Chapter 1 / Whole Numbers and Introduction to Algebra
Addition Property of Equality
Let a, b, and c represent numbers.
If a = b, then
a + c = b + c
and
a – c = b - c
In other words, the same number may be added to or subtracted from both sides of an equation without changing the solution of the equation.
Martin-Gay, Prealgebra, 5ed

3. Multiplication Property of Equality
Chapter 1 / Whole Numbers and Introduction to Algebra
Multiplication Property of Equality
Let a, b, and c represent numbers and let c  0. If a = b, then
a  c = b  c and
In other words, both sides of an equation may be multiplied or divided by the same nonzero number without changing the solution of the equation.
Martin-Gay, Prealgebra, 5ed

4. Solving an Equation in x
Chapter 1 / Whole Numbers and Introduction to Algebra
Solving an Equation in x
Step 1. If fractions are present, multiply both sides of the equation by the LCD of the fractions.
Step 2. If parentheses are present, use the distributive property.
Step 3. Combine any like terms on each side of the equation.
Martin-Gay, Prealgebra, 5ed

5. Solving an Equation in x . . .
Chapter 1 / Whole Numbers and Introduction to Algebra
Solving an Equation in x . . .
Step 4. Use the addition property of equality to rewrite the equation so that variable terms are on one side of the equation and constant terms are on the other side.
Step 5. Divide both sides of the equation by the numerical coefficient of x to solve.
Step 6. Check the answer in the original equation.
Martin-Gay, Prealgebra, 5ed

6. Chapter 1 / Whole Numbers and Introduction to Algebra
Solve for x
Multiply both sides by 7.
Simplify both sides.
Martin-Gay, Prealgebra, 5ed

7. Chapter 1 / Whole Numbers and Introduction to Algebra
Solve for x
Multiply both sides by 5.
Simplify both sides.
Add – 3y to both sides.
Add – 30 to both sides.
Divide both sides by 7.
Martin-Gay, Prealgebra, 5ed