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

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

Multiply both sides by $4$ .

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

Simplify.

Simplify the left side.

Simplify $(2 x + 3) \cdot 4$ .

Apply the distributive property.

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

Multiply.

Multiply $4$ by $2$ .

$8 x + 3 \cdot 4 = \frac{x}{4} \cdot 4$

Multiply $3$ by $4$ .

$8 x + 12 = \frac{x}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$8 x + 12 = \frac{x}{4} \cdot 4$

Rewrite the expression.

$8 x + 12 = x$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$8 x + 12 - x = 0$

Subtract $x$ from $8 x$ .

$7 x + 12 = 0$

Subtract $12$ from both sides of the equation.

$7 x = - 12$

Divide each term in $7 x = - 12$ by $7$ and simplify.

Divide each term in $7 x = - 12$ by $7$ .

$\frac{7 x}{7} = \frac{- 12}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 12}{7}$

Divide $x$ by $1$ .

$x = \frac{- 12}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{12}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{7}$

Decimal Form:

$x = - 1.\overline{714285}$

Mixed Number Form:

$x = - 1 \frac{5}{7}$

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

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