Solve for x 9/4=(7x+6)/2

$\frac{9}{4} = \frac{7 x + 6}{2}$

Rewrite the equation as $\frac{7 x + 6}{2} = \frac{9}{4}$ .

$\frac{7 x + 6}{2} = \frac{9}{4}$

Multiply both sides by $2$ .

$\frac{7 x + 6}{2} \cdot 2 = \frac{9}{4} \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 x + 6}{2} \cdot 2 = \frac{9}{4} \cdot 2$

Rewrite the expression.

$7 x + 6 = \frac{9}{4} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$7 x + 6 = \frac{9}{2 (2)} \cdot 2$

Cancel the common factor.

$7 x + 6 = \frac{9}{2 \cdot 2} \cdot 2$

Rewrite the expression.

$7 x + 6 = \frac{9}{2}$

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$7 x = \frac{9}{2} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 x = \frac{9}{2} - 6 \cdot \frac{2}{2}$

Combine $- 6$ and $\frac{2}{2}$ .

$7 x = \frac{9}{2} + \frac{- 6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$7 x = \frac{9 - 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 6$ by $2$ .

$7 x = \frac{9 - 12}{2}$

Subtract $12$ from $9$ .

$7 x = \frac{- 3}{2}$

Move the negative in front of the fraction.

$7 x = - \frac{3}{2}$

Divide each term in $7 x = - \frac{3}{2}$ by $7$ and simplify.

Divide each term in $7 x = - \frac{3}{2}$ by $7$ .

$\frac{7 x}{7} = \frac{- \frac{3}{2}}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- \frac{3}{2}}{7}$

Divide $x$ by $1$ .

$x = \frac{- \frac{3}{2}}{7}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{2} \cdot \frac{1}{7}$

Multiply $- \frac{3}{2} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{3}{2}$ .

$x = - \frac{3}{7 \cdot 2}$

Multiply $7$ by $2$ .

$x = - \frac{3}{14}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{14}$

Decimal Form:

$x = - 0.2\overline{142857}$

Solve for x 9/4=(7x+6)/2

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