Solve the Rational Equation for x x/3+1/4=x/2

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

Step 1

Multiply both sides by $2$ .

$(\frac{x}{3} + \frac{1}{4}) \cdot 2 = \frac{x}{2} \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{x}{3} + \frac{1}{4}) \cdot 2$ .

Simplify terms.

Apply the distributive property.

$\frac{x}{3} \cdot 2 + \frac{1}{4} \cdot 2 = \frac{x}{2} \cdot 2$

Combine $\frac{x}{3}$ and $2$ .

$\frac{x \cdot 2}{3} + \frac{1}{4} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{x \cdot 2}{3} + \frac{1}{2 (2)} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor.

$\frac{x \cdot 2}{3} + \frac{1}{2 \cdot 2} \cdot 2 = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{x \cdot 2}{3} + \frac{1}{2} = \frac{x}{2} \cdot 2$

Move $2$ to the left of $x$ .

$\frac{2 x}{3} + \frac{1}{2} = \frac{x}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{3} + \frac{1}{2} = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{2 x}{3} + \frac{1}{2} = x$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\frac{2 x}{3} + \frac{1}{2} - x = 0$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} - x \cdot \frac{3}{3} + \frac{1}{2} = 0$

Combine $- x$ and $\frac{3}{3}$ .

$\frac{2 x}{3} + \frac{- x \cdot 3}{3} + \frac{1}{2} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - x \cdot 3}{3} + \frac{1}{2} = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x - x \cdot 3$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2 - x \cdot 3}{3} + \frac{1}{2} = 0$

Factor $x$ out of $- x \cdot 3$ .

$\frac{x \cdot 2 + x (- 1 \cdot 3)}{3} + \frac{1}{2} = 0$

Factor $x$ out of $x \cdot 2 + x (- 1 \cdot 3)$ .

$\frac{x (2 - 1 \cdot 3)}{3} + \frac{1}{2} = 0$

Multiply $- 1$ by $3$ .

$\frac{x (2 - 3)}{3} + \frac{1}{2} = 0$

Subtract $3$ from $2$ .

$\frac{x \cdot - 1}{3} + \frac{1}{2} = 0$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{3} + \frac{1}{2} = 0$

Move the negative in front of the fraction.

$- \frac{x}{3} + \frac{1}{2} = 0$

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{x}{3} = - \frac{1}{2}$

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{x}{3}) = - 3 (- \frac{1}{2})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 (- \frac{1}{2})$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 (- \frac{1}{2})$

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 (- \frac{1}{2})$

Rewrite the expression.

$- - x = - 3 (- \frac{1}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 (- \frac{1}{2})$

Multiply $x$ by $1$ .

$x = - 3 (- \frac{1}{2})$

Simplify the right side.

Multiply $- 3 (- \frac{1}{2})$ .

Multiply $- 1$ by $- 3$ .

$x = 3 (\frac{1}{2})$

Combine $3$ and $\frac{1}{2}$ .

$x = \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

Solve the Rational Equation for x x/3+1/4=x/2

Related Questions

Support LCMGCF.com by disabling your adblocker.