The equation given is:

\[
\frac{3x - 4}{8} = \frac{2x - 6}{7}
\]

To solve for \( x \), follow these steps:

1. **Cross-multiply** to eliminate the fractions:
   \[
   7(3x - 4) = 8(2x - 6)
   \]

2. **Expand** both sides:
   \[
   21x - 28 = 16x - 48
   \]

3. **Isolate the variable** \( x \):
   - Subtract \( 16x \) from both sides:
     \[
     21x - 16x - 28 = -48
     \]
     \[
     5x - 28 = -48
     \]
   - Add 28 to both sides:
     \[
     5x = -20
     \]

4. **Solve for \( x \)**:
   \[
   x = \frac{-20}{5} = -4
   \]

So, the solution is \( x = -4 \).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would you solve the equation if there were different constants in the numerators?
2. What if the equation were \( \frac{3x + 4}{8} = \frac{2x + 6}{7} \)?
3. How can you check if the solution \( x = -4 \) is correct?
4. How would the solution change if one of the fractions had a negative denominator?
5. Can you solve the equation if the variables were on the denominator instead?

**Tip:** Always simplify the equation step by step to avoid errors when dealing with fractions.

Solve the equation: (3x - 4)/8 = (2x - 6)/7

Learn how to solve the linear equation (3x - 4)/8 = (2x - 6)/7 with a step-by-step guide. This solution involves cross-multiplication, expanding, and isolating the variable x. Perfect for students in Grades 8-10 who are practicing algebraic techniques with fractions.

Math Problem Statement

3x−4 8

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