7x - 1 - 1(4x - 1 - x) = 10/3

Steps to Solve

1. Rewrite the equation for clarity

Start with the equation:

$$ \frac{7x - 1}{4} - \frac{1}{3}(4x - 1 - x) = \frac{10}{3} $$

2. Distribute the fraction

Distribute the $\frac{1}{3}$ to the terms inside the parentheses:

$$ \frac{7x - 1}{4} - \left(\frac{4x}{3} - \frac{1}{3} - \frac{x}{3}\right) = \frac{10}{3} $$

This simplifies to:

$$ \frac{7x - 1}{4} - \left(\frac{4x - x}{3} - \frac{1}{3}\right) = \frac{10}{3} $$

Which further reduces to:

$$ \frac{7x - 1}{4} - \left(\frac{3x - 1}{3}\right) = \frac{10}{3} $$

3. Get a common denominator

To simplify the equation further, find a common denominator for the left side:

The common denominator between 4 and 3 is 12.

Rewrite the fractions:

$$ \frac{3(7x - 1)}{12} - \frac{4(3x - 1)}{12} = \frac{10}{3} $$

4. Combine the fractions

Now combine the fractions on the left side:

$$ \frac{3(7x - 1) - 4(3x - 1)}{12} = \frac{10}{3} $$

Distributing gives us:

$$ \frac{21x - 3 - 12x + 4}{12} = \frac{10}{3} $$

Simplifying the numerator:

$$ \frac{9x + 1}{12} = \frac{10}{3} $$

5. Eliminate the fraction by multiplying

Multiply both sides by 12 to eliminate the denominator:

$$ 9x + 1 = 40 $$

6. Isolate x

Subtract 1 from both sides:

$$ 9x = 39 $$

Now divide by 9:

$$ x = \frac{39}{9} = \frac{13}{3} $$