Solve for x 5/4+(3x)/2=(7x)/6

$\frac{5}{4} + \frac{3 x}{2} = \frac{7 x}{6}$

Multiply both sides by $6$ .

$(\frac{5}{4} + \frac{3 x}{2}) \cdot 6 = \frac{7 x}{6} \cdot 6$

Simplify.

Simplify the left side.

Simplify $(\frac{5}{4} + \frac{3 x}{2}) \cdot 6$ .

Apply the distributive property.

$\frac{5}{4} \cdot 6 + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{5}{2 (2)} \cdot 6 + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Factor $2$ out of $6$ .

$\frac{5}{2 \cdot 2} \cdot (2 \cdot 3) + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Cancel the common factor.

$\frac{5}{2 \cdot 2} \cdot (2 \cdot 3) + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Rewrite the expression.

$\frac{5}{2} \cdot 3 + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Combine $\frac{5}{2}$ and $3$ .

$\frac{5 \cdot 3}{2} + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Multiply $5$ by $3$ .

$\frac{15}{2} + \frac{3 x}{2} \cdot 6 = \frac{7 x}{6} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{15}{2} + \frac{3 x}{2} \cdot (2 (3)) = \frac{7 x}{6} \cdot 6$

Cancel the common factor.

$\frac{15}{2} + \frac{3 x}{2} \cdot (2 \cdot 3) = \frac{7 x}{6} \cdot 6$

Rewrite the expression.

$\frac{15}{2} + 3 x \cdot 3 = \frac{7 x}{6} \cdot 6$

Simplify the expression.

Multiply $3$ by $3$ .

$\frac{15}{2} + 9 x = \frac{7 x}{6} \cdot 6$

Reorder $\frac{15}{2}$ and $9 x$ .

$9 x + \frac{15}{2} = \frac{7 x}{6} \cdot 6$

Simplify the right side.

Cancel the common factor of $6$ .

Cancel the common factor.

$9 x + \frac{15}{2} = \frac{7 x}{6} \cdot 6$

Rewrite the expression.

$9 x + \frac{15}{2} = 7 x$

Solve for $x$ .

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

Subtract $7 x$ from both sides of the equation.

$9 x + \frac{15}{2} - 7 x = 0$

Subtract $7 x$ from $9 x$ .

$2 x + \frac{15}{2} = 0$

Subtract $\frac{15}{2}$ from both sides of the equation.

$2 x = - \frac{15}{2}$

Divide each term in $2 x = - \frac{15}{2}$ by $2$ and simplify.

Divide each term in $2 x = - \frac{15}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{15}{2}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{15}{2}}{2}$

Divide $x$ by $1$ .

$x = \frac{- \frac{15}{2}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{15}{2} \cdot \frac{1}{2}$

Multiply $- \frac{15}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{15}{2}$ .

$x = - \frac{15}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = - \frac{15}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{4}$

Decimal Form:

$x = - 3.75$

Mixed Number Form:

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

Solve for x 5/4+(3x)/2=(7x)/6

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