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Solving Linear Equations Containing Fractions

Solve:

Solution

First, find the LCD of the fractions.

Step 1 Factor each denominator into its prime factors.

Step 2 List each factor the greatest number of times that it appears in any one of the denominators.

Step 3 Multiply the prime factors in the list.

So, the LCD of the fractions is 40.

8 = 2 · 2 ·2

20 = 2 · 2 · 5

10 = 2 · 5

2, 2, 2, 5

2 · 2 · 2 · 5 = 40

Next, clear the fractions:
• Multiply each side by the LCD, 40.
• Simplify. 5x = 2x - 4
Then, solve the equation for x:

• Subtract 2x from both sides.

3x = -4
• Divide both sides by 3.

We leave the check to you.

The solution is .

Note: can also be written as