Which number can each term of the equation be multiplied by to eliminate the fractions before solving?

6 – x +  = 6 minus StartFraction 3 Over 4 EndFraction x plus StartFraction 1 Over 3 EndFraction equals StartFraction one-half EndFraction x plus 5.x + 5

To eliminate the fractions in the equation

\[
6 - \frac{3}{4}x + \frac{1}{3} = \frac{1}{2}x + 5
\]

you need to find the least common denominator (LCD) of all the denominators: 4, 3, and 2.

### Step 1: Find the LCD
The denominators are 4, 3, and 2. The least common denominator (LCD) of 4, 3, and 2 is 12.

### Step 2: Multiply every term by 12
Multiplying both sides of the equation by 12 will eliminate the fractions:

\[
12(6) - 12\left(\frac{3}{4}x\right) + 12\left(\frac{1}{3}\right) = 12\left(\frac{1}{2}x\right) + 12(5)
\]

### Step 3: Simplify the terms
\[
12 \cdot 6 - \frac{12 \cdot 3}{4}x + \frac{12 \cdot 1}{3} = \frac{12 \cdot 1}{2}x + 12 \cdot 5
\]
\[
72 - 9x + 4 = 6x + 60
\]

Now, the equation no longer contains fractions and can be solved further.

Would you like to proceed with solving the equation or need more details?

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Here are 5 related questions to expand your understanding:

1. What is the least common denominator (LCD) and how do you calculate it?
2. How do you solve linear equations after eliminating fractions?
3. Can you apply the same technique of multiplying by the LCD for systems of equations?
4. How do you verify that the solution to an equation is correct?
5. What are some common mistakes to avoid when working with equations containing fractions?

**Tip:** Always check your work after eliminating fractions by plugging values back into the original equation to verify correctness.

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6 - (3/4)x + (1/3) = (1/2)x + 5

Learn how to eliminate fractions in an algebraic equation by finding the least common denominator (LCD). This example involves the equation 6 - (3/4)x + (1/3) = (1/2)x + 5, where we multiply all terms by 12 to simplify and solve. Suitable for students in Grades 8-10.

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