If (5x - 7)/3 + 2 = (4x - 3)/4 + 4x, then the value of (8x + 5) is:

For a linear equation containing fractions, first clear every denominator by multiplying both sides of the equation by their least common multiple (LCM). This produces an equivalent equation with integer coefficients only, which can then be simplified by expanding, collecting like terms, and isolating the variable.

1. Multiply every term of (5x − 7)/3 + 2 = (4x − 3)/4 + 4x by 12, the LCM of 3 and 4: 4(5x − 7) + 24 = 3(4x − 3) + 48x.

2. Expand both sides: 20x − 28 + 24 = 12x − 9 + 48x.

3. Combine like terms: 20x − 4 = 60x − 9.

4. Collect the x-terms on one side and the constants on the other: 5 = 40x.

5. Solve for x: x = 5/40 = 1/8.

6. Substitute x = 1/8 into the required expression: 8x + 5 = 8 × (1/8) + 5 = 1 + 5 = 6.

Substituting x = 1/8 back into the original equation confirms the solution: the left side, (5×1/8 − 7)/3 + 2, equals −1/8, and the right side, (4×1/8 − 3)/4 + 4×1/8, also equals −1/8, so both sides balance.

Therefore, the value of (8x + 5) is 6.