1. Solving Equations with Fractions
Section 2.4
Solving Equations with Fractions

2. Example Solve for a.  Multiply both sides by 4. Simplify.
Add 2a to both sides.
Divide both sides by 3.
Check your answer in the original equation. 

3. Example Solve for x. Distribute to remove parentheses. The LCD is 12.
Simplify.
Combine like terms.
Add 9x and subtract 32 from each side.
Divide both sides by 17. 3

4. Example
Solve for x.
Be sure to check your answer!

5. Procedure to Solve Equations
1. Remove any parentheses.
2. If fractions exist, multiply all terms on both sides by the LCD of the fractions.
3. Combine like terms, if possible.
4. Add or subtract terms on both sides of the equation to get all terms with the variable on one side of the equation.
5. Add or subtract a constant value on both sides of the equation to get all terms not containing the variable on the other side of the equation.
6. Divide both sides of the equation by the coefficient of the variable.
7. Simplify the solution (if possible).
8. Check your solution.

6. Example Solve for x. 0.2(1 – 8x) + 1.1 = –5(0.4x – 0.3)
Remove parentheses.
10(0.2) – 10(1.6x) + 10(1.1) = 10(–2.0x) + 10(1.5)
2 –16x + 11 = –20x + 15
–16x + 13 = –20x + 15
Simplify.
–16x + 20x + 13 = –20x + 20x + 15
4x + 13 = 15
4x + 13 = 15 – 13
4x = 2
The answer checks!

7. Solutions
There are some cases where an equation has no solution at all.
An equation may also have an infinite number of solutions.

8. Example Solve for y. This equation has no solution.
– 1 + 5(y – 2) = 12y + 3 – 7y
Distribute to remove the parentheses.
– 1 + 5y – 10 = 12y + 3 – 7y
5y – 11 = 5y + 3
Combine like terms.
– 11 = 3
Subtract 5y from both sides.
False!
This equation has no solution.

9. Example
Solve for z.
7(z + 4) – 10 = 3z z – 2
Distribute to remove the parentheses.
7z + 28 – 10 = 3z z – 2
7z + 18 = 7z + 18
Combine like terms.
18 = 18
Subtract 7z from both sides.
Always true.
This equation has an infinite number of solutions.