If x satisfies the linear equation \frac{2(3x - 1)}{5} - \frac{4x - 3}{3} = \frac{x + 18}{… — GRE General Test

x

satisfies the linear equation

\frac{2(3x - 1)}{5} - \frac{4x - 3}{3} = \frac{x + 18}{15} - 2

what is the value of

3x - 5

Multiplying the entire equation by the common denominator

15

clears all fractions, yielding

6(3x - 1) - 5(4x - 3) = (x + 18) - 30

. Expanding both sides produces

18x - 6 - 20x + 15 = x - 12

, which simplifies to

-2x + 9 = x - 12

. Rearranging terms yields

-3x = -21

, so

x = 7

. Substituting

x = 7

into

3x - 5

gives

3(7) - 5 = 16

Clear the denominators by multiplying both sides of the equation by the least common multiple (LCM) of 5, 3, and 15, which is 15.

15 \cdot \left(\frac{2(3x - 1)}{5}\right) - 15 \cdot \left(\frac{4x - 3}{3}\right) = 15 \cdot \left(\frac{x + 18}{15}\right) - 15 \cdot 2

Eliminating fractions simplifies the linear equation into standard integer polynomial terms.

Simplify the products and distribute coefficients across parentheses.

3 \cdot 2(3x - 1) - 5(4x - 3) = (x + 18) - 30 \implies 6(3x - 1) - 5(4x - 3) = x - 12

Perform fractional reduction and simplify constants on the right side.

Expand both groupings and combine like terms on the left-hand side.

18x - 6 - 20x + 15 = x - 12 \implies -2x + 9 = x - 12

Ensure the negative sign is properly distributed to both terms inside

-5(4x - 3)

Isolate the variable

x

by subtracting

x

and

9

from both sides.

-3x = -21 \implies x = 7

Solve for the single variable

x

Substitute

x = 7

into the target expression

3x - 5

3(7) - 5 = 21 - 5 = 16

The question asks for the value of the algebraic expression

3x - 5

, not

x

alone.

Linear Equations in One Variable with Fractional Coefficients

Estimated Time:2m 0s

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