To solve the equation \(\frac{1}{2}x - 5 = 10 - \frac{3}{4}x\), follow these steps:

1. **Eliminate the fractions** by finding a common denominator. The least common denominator between \(\frac{1}{2}\) and \(\frac{3}{4}\) is 4. Multiply every term by 4 to eliminate the fractions:
   \[
   4 \times \left(\frac{1}{2}x\right) - 4 \times 5 = 4 \times 10 - 4 \times \left(\frac{3}{4}x\right)
   \]
   Simplifying, we get:
   \[
   2x - 20 = 40 - 3x
   \]

2. **Add \(3x\) to both sides** to bring the \(x\) terms together on one side:
   \[
   2x + 3x - 20 = 40 - 3x + 3x
   \]
   Simplifying, we get:
   \[
   5x - 20 = 40
   \]

3. **Add 20 to both sides** to isolate the \(x\) term:
   \[
   5x - 20 + 20 = 40 + 20
   \]
   Simplifying, we get:
   \[
   5x = 60
   \]

4. **Divide both sides by 5** to solve for \(x\):
   \[
   x = \frac{60}{5}
   \]
   Simplifying, we get:
   \[
   x = 12
   \]

So, the solution is \(x = 12\).

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the result if you substitute \(x = 12\) back into the original equation?
2. How would the solution change if the equation were \(\frac{1}{2}x - 5 = 10 + \frac{3}{4}x\)?
3. Can you solve the equation if the coefficients were different fractions?
4. What if the equation involved decimals instead of fractions?
5. How would you graph the equation \(\frac{1}{2}x - 5 = 10 - \frac{3}{4}x\)?

**Tip:** When dealing with fractions in equations, multiplying every term by the least common denominator is a quick way to eliminate the fractions and simplify the equation.

Learn how to solve the equation 1/2x - 5 = 10 - 3/4x with a detailed step-by-step solution. This problem involves solving equations with fractions, suitable for students studying algebra in Grades 7-9.

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