Solve for x -5=3 1/2x

$- 5 = 3 \frac{1}{2} x$

Simplify the right side.

Simplify $3 \frac{1}{2} x$ .

Convert $3 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- 5 = (3 + \frac{1}{2}) x$

Add $3$ and $\frac{1}{2}$ .

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

$- 5 = (3 \cdot \frac{2}{2} + \frac{1}{2}) x$

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

$- 5 = (\frac{3 \cdot 2}{2} + \frac{1}{2}) x$

Combine the numerators over the common denominator.

$- 5 = \frac{3 \cdot 2 + 1}{2} x$

Simplify the numerator.

Multiply $3$ by $2$ .

$- 5 = \frac{6 + 1}{2} x$

Add $6$ and $1$ .

$- 5 = \frac{7}{2} x$

Combine $\frac{7}{2}$ and $x$ .

$- 5 = \frac{7 x}{2}$

Rewrite the equation as $\frac{7 x}{2} = - 5$ .

$\frac{7 x}{2} = - 5$

Multiply both sides of the equation by $\frac{2}{7}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{7} \cdot \frac{7 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot - 5$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot - 5$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot - 5$

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{2}{7} \cdot - 5$ .

Multiply $\frac{2}{7} \cdot - 5$ .

Combine $\frac{2}{7}$ and $- 5$ .

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

Multiply $2$ by $- 5$ .

$x = \frac{- 10}{7}$

Move the negative in front of the fraction.

$x = - \frac{10}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{10}{7}$

Decimal Form:

$x = - 1.\overline{428571}$

Mixed Number Form:

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

Solve for x -5=3 1/2x

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