Solve for x (3x)/4+3/2=5/14

$\frac{3 x}{4} + \frac{3}{2} = \frac{5}{14}$

Step 1

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

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{3 x}{4} = \frac{5}{14} - \frac{3}{2}$

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 x}{4} = \frac{5}{14} - \frac{3}{2} \cdot \frac{7}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 x}{4} = \frac{5}{14} - \frac{3 \cdot 7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{3 x}{4} = \frac{5}{14} - \frac{3 \cdot 7}{14}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{5 - 3 \cdot 7}{14}$

Simplify the numerator.

Multiply $- 3$ by $7$ .

$\frac{3 x}{4} = \frac{5 - 21}{14}$

Subtract $21$ from $5$ .

$\frac{3 x}{4} = \frac{- 16}{14}$

Cancel the common factor of $- 16$ and $14$ .

Factor $2$ out of $- 16$ .

$\frac{3 x}{4} = \frac{2 (- 8)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$\frac{3 x}{4} = \frac{2 \cdot - 8}{2 \cdot 7}$

Cancel the common factor.

$\frac{3 x}{4} = \frac{2 \cdot - 8}{2 \cdot 7}$

Rewrite the expression.

$\frac{3 x}{4} = \frac{- 8}{7}$

Move the negative in front of the fraction.

$\frac{3 x}{4} = - \frac{8}{7}$

Step 2

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{8}{7})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{8}{7})$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{8}{7})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} (- \frac{8}{7})$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{8}{7})$

Rewrite the expression.

$x = \frac{4}{3} (- \frac{8}{7})$

Simplify the right side.

Multiply $\frac{4}{3} (- \frac{8}{7})$ .

Multiply $\frac{4}{3}$ by $\frac{8}{7}$ .

$x = - \frac{4 \cdot 8}{3 \cdot 7}$

Multiply $4$ by $8$ .

$x = - \frac{32}{3 \cdot 7}$

Multiply $3$ by $7$ .

$x = - \frac{32}{21}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{32}{21}$

Decimal Form:

$x = - 1.\overline{523809}$

Mixed Number Form:

$x = - 1 \frac{11}{21}$

Solve for x (3x)/4+3/2=5/14

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