If x satisfies the linear equation \frac{3(x - 4)}{4} - \frac{2x + 1}{6} = \frac{x + 2}{3}… — GRE General Test

x

satisfies the linear equation

\frac{3(x - 4)}{4} - \frac{2x + 1}{6} = \frac{x + 2}{3} - 5

what is the value of

2x + 5

The value of

2x + 5

-23

Clearing denominators by multiplying the entire equation by

12

gives

9(x - 4) - 2(2x + 1) = 4(x + 2) - 60

. Expanding both sides yields

9x - 36 - 4x - 2 = 4x + 8 - 60

, which simplifies to

5x - 38 = 4x - 52

. Isolating

x

gives

x = -14

. Substituting

x = -14

into the target expression

2x + 5

yields

2(-14) + 5 = -23

Clear the denominators by multiplying every term on both sides of the equation by the least common multiple of

4, 6,

and

3

, which is

12

12 \cdot \frac{3(x - 4)}{4} - 12 \cdot \frac{2x + 1}{6} = 12 \cdot \frac{x + 2}{3} - 12 \cdot 5

, leading to

9(x - 4) - 2(2x + 1) = 4(x + 2) - 60

Clearing denominators simplifies the multi-step fractional equation into an integer linear equation.

Expand all grouping symbols and combine like terms on both sides.

9x - 36 - 4x - 2 = 4x + 8 - 60

, which simplifies to

5x - 38 = 4x - 52

Distributing terms carefully ensures proper sign distribution, especially for negative signs across parentheses.

Isolate the variable

x

on one side of the equation.

5x - 4x = -52 + 38

, giving

x = -14

Subtracting

4x

and adding

38

isolates

x

Evaluate the target expression

2x + 5

using the solved value

x = -14

2(-14) + 5 = -28 + 5 = -23

The question asks for the value of

2x + 5

, not

x

Solving linear equations in one variable with fractional coefficients and evaluating algebraic expressions

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