If \frac{x}{2} + \frac{x}{3} = 10, what is the value of x? — GRE General Test

If $\frac{x}{2} + \frac{x}{3} = 10$ , what is the value of $x$ ?

The value of

x

is 12.

The option showing 12 is correct because converting the fractions

\frac{x}{2}

and

\frac{x}{3}

to have a common denominator of 6 produces

\frac{3x + 2x}{6} = 10

, or

\frac{5x}{6} = 10

. Multiplying both sides by 6 gives

5x = 60

, and dividing by 5 yields

x = 12

Find a common denominator for the fractional terms on the left side of the equation.

The least common denominator of 2 and 3 is 6. Rewriting the fractions gives

\frac{3x}{6} + \frac{2x}{6} = 10

Fractions must have identical denominators before their numerators can be added.

Combine the fractions on the left side.

\frac{5x}{6} = 10

Adding the numerators

3x + 2x

yields

5x

over the shared denominator 6.

Clear the denominator by multiplying both sides of the equation by 6.

5x = 60

Multiplying both sides by 6 eliminates the fraction while maintaining equality.

Isolate

x

by dividing both sides by 5.

x = 12

Dividing 60 by 5 yields the solution for

x

Solving linear equations involving fractions by clearing denominators using the least common multiple.

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