Sure, let's solve the equation step-by-step:
We have:
[tex]\[
\frac{4x - 8}{6} = \frac{3x - 4}{5}
\][/tex]
Step 1: Eliminate the fractions by finding a common denominator.
The common denominator of 6 and 5 is 30. Multiply both sides of the equation by 30:
[tex]\[
30 \cdot \frac{4x - 8}{6} = 30 \cdot \frac{3x - 4}{5}
\][/tex]
Step 2: Simplify both sides.
Distribute the 30 through the fractions:
[tex]\[
30 \cdot \frac{4x - 8}{6} = \frac{30 \cdot (4x - 8)}{6} = 5 \cdot (4x - 8)
\][/tex]
[tex]\[
30 \cdot \frac{3x - 4}{5} = \frac{30 \cdot (3x - 4)}{5} = 6 \cdot (3x - 4)
\][/tex]
Therefore, the equation simplifies to:
[tex]\[
5(4x - 8) = 6(3x - 4)
\][/tex]
Step 3: Distribute the constants on both sides.
Apply the distributive property:
[tex]\[
5 \cdot 4x - 5 \cdot 8 = 6 \cdot 3x - 6 \cdot 4
\][/tex]
[tex]\[
20x - 40 = 18x - 24
\][/tex]
Step 4: Move all terms involving [tex]\(x\)[/tex] to one side of the equation and constants to the other side.
Subtract [tex]\(18x\)[/tex] from both sides:
[tex]\[
20x - 40 - 18x = 18x - 24 - 18x
\][/tex]
[tex]\[
2x - 40 = -24
\][/tex]
Add 40 to both sides:
[tex]\[
2x - 40 + 40 = -24 + 40
\][/tex]
[tex]\[
2x = 16
\][/tex]
Step 5: Solve for [tex]\(x\)[/tex] by isolating it.
Divide both sides by 2:
[tex]\[
x = \frac{16}{2}
\][/tex]
[tex]\[
x = 8
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = 8
\][/tex]
