If x satisfies the equation \frac{x + 5}{3} - 2 = \frac{x - 1}{4}, what is the value of x? — GRE General Test

If $x$ satisfies the equation $\frac{x + 5}{3} - 2 = \frac{x - 1}{4}$ , what is the value of $x$ ?

Multiplying the equation

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

by the common denominator

12

eliminates fractions to produce

4(x + 5) - 24 = 3(x - 1)

. Expanding both sides yields

4x + 20 - 24 = 3x - 3

, which simplifies to

4x - 4 = 3x - 3

. Subtracting

3x

from both sides and adding

4

to both sides gives

x = 1

Multiply every term on both sides of the equation by the least common denominator of 3 and 4, which is 12.

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

, which simplifies to

4(x + 5) - 24 = 3(x - 1)

Clearing fractional denominators simplifies the equation into integer-coefficient linear form.

Expand both sides by distributing the numeric multipliers.

4x + 20 - 24 = 3x - 3

, which combines like terms to

4x - 4 = 3x - 3

Distributing coefficients removes grouping symbols so variable and constant terms can be combined.

Isolate the variable term

x

on one side.

Subtract

3x

from both sides to get

x - 4 = -3

, then add

4

to both sides to get

x = 1

Standard algebraic reduction requires grouping all terms containing the unknown variable on one side and numerical constants on the other.

Solving single-variable linear equations containing fractional terms by clearing denominators

Estimated Time:1m 0s

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