https://file.aiquickdraw.com/mathbot/file/1726929281908c6t1yqs8.jpg

The equation in the image is:

\[
\frac{3}{4}x - \frac{1}{2} = 7
\]

### Let's solve it step by step:

1. Start by isolating the term involving \(x\). Add \(\frac{1}{2}\) to both sides:
   \[
   \frac{3}{4}x = 7 + \frac{1}{2}
   \]

2. To add \(7 + \frac{1}{2}\), convert \(7\) to a fraction with the same denominator:
   \[
   7 = \frac{14}{2}, \quad \text{so} \quad \frac{14}{2} + \frac{1}{2} = \frac{15}{2}
   \]
   Therefore:
   \[
   \frac{3}{4}x = \frac{15}{2}
   \]

3. Now, solve for \(x\) by multiplying both sides of the equation by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):
   \[
   x = \frac{15}{2} \times \frac{4}{3}
   \]

4. Multiply the fractions:
   \[
   x = \frac{15 \times 4}{2 \times 3} = \frac{60}{6} = 10
   \]

Thus, the solution is:

\[
x = 10
\]

Would you like further details on any part of the solution?

Here are 5 related questions:
1. How do you solve equations with fractions?
2. What is the significance of multiplying by the reciprocal?
3. How can you simplify complex fractions more efficiently?
4. Why do we need to balance both sides of an equation?
5. What other methods can be used to solve linear equations?

**Tip:** Always convert mixed numbers or whole numbers to fractions when dealing with fractional equations to simplify calculations.

Learn how to solve the linear equation (3/4)x - 1/2 = 7 step by step. This problem involves algebraic concepts such as fraction manipulation, isolating variables, and reciprocal multiplication. Ideal for students in Grades 8-10.

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