If x satisfies the linear equation \frac{x + 2}{2} + \frac{x - 1}{3} = 4, what is the valu… — GRE General Test

If $x$ satisfies the linear equation $\frac{x + 2}{2} + \frac{x - 1}{3} = 4$ , what is the value of $3x - 2$ ?

The value of

3x - 2

10

To solve

\frac{x + 2}{2} + \frac{x - 1}{3} = 4

, multiply the entire equation by the common denominator 6 to clear fractions, yielding

3(x + 2) + 2(x - 1) = 24

. Distributing gives

3x + 6 + 2x - 2 = 24

, which simplifies to

5x + 4 = 24 \implies 5x = 20 \implies x = 4

. Substituting

x = 4

into

3x - 2

gives

3(4) - 2 = 10

Find a common denominator to clear the fractions from the equation.

The least common multiple of 2 and 3 is 6. Multiplying both sides of the equation by 6 gives

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

, which simplifies to

3(x + 2) + 2(x - 1) = 24

Clearing denominators simplifies multi-step fractional equations into standard linear form.

Expand terms and solve for

x

3x + 6 + 2x - 2 = 24 \implies 5x + 4 = 24 \implies 5x = 20 \implies x = 4

Combining like terms isolates the variable

x

Substitute

x = 4

into the target expression

3x - 2

3(4) - 2 = 12 - 2 = 10

The question asks for the value of the algebraic expression

3x - 2

, not

x

itself.

Solving linear equations with fractional coefficients by clearing denominators and evaluating target algebraic expressions.

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