Solve the Rational Equation for x (x+3)/2-x/4=4/3

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

Step 1

Simplify $\frac{x + 3}{2} - \frac{x}{4}$ .

To write $\frac{x + 3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 3}{2}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $3$ by $2$ .

$\frac{2 \cdot x + 6 - x}{4} = \frac{4}{3}$

Subtract $x$ from $2 x$ .

$\frac{x + 6}{4} = \frac{4}{3}$

Step 2

Multiply both sides of the equation by $4$ .

$4 \frac{x + 6}{4} = 4 (\frac{4}{3})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x + 6}{4} = 4 (\frac{4}{3})$

Rewrite the expression.

$x + 6 = 4 (\frac{4}{3})$

Simplify the right side.

Multiply $4 (\frac{4}{3})$ .

Combine $4$ and $\frac{4}{3}$ .

$x + 6 = \frac{4 \cdot 4}{3}$

Multiply $4$ by $4$ .

$x + 6 = \frac{16}{3}$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$x = \frac{16}{3} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{16}{3} - 6 \cdot \frac{3}{3}$

Combine $- 6$ and $\frac{3}{3}$ .

$x = \frac{16}{3} + \frac{- 6 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{16 - 6 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 6$ by $3$ .

$x = \frac{16 - 18}{3}$

Subtract $18$ from $16$ .

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

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{6}$

Solve the Rational Equation for x (x+3)/2-x/4=4/3

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