Solve for x x/2-1=(3-x)/5

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

Multiply both sides by $5$ .

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

Simplify.

Simplify the left side.

Simplify $(\frac{x}{2} - 1) \cdot 5$ .

Simplify terms.

Apply the distributive property.

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

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

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

Multiply $- 1$ by $5$ .

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

Move $5$ to the left of $x$ .

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

Simplify the right side.

Simplify $\frac{3 - x}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Reorder $3$ and $- x$ .

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

Solve for $x$ .

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

Add $x$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $5 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Add $5 x$ and $2 \cdot x$ .

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

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

Add $5$ to both sides of the equation.

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

Add $3$ and $5$ .

$\frac{7 x}{2} = 8$

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

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 8$

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.

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 8$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 8$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot 8$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 8$

Rewrite the expression.

$x = \frac{2}{7} \cdot 8$

Simplify the right side.

Multiply $\frac{2}{7} \cdot 8$ .

Combine $\frac{2}{7}$ and $8$ .

$x = \frac{2 \cdot 8}{7}$

Multiply $2$ by $8$ .

$x = \frac{16}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{7}$

Decimal Form:

$x = 2.\overline{285714}$

Mixed Number Form:

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

Solve for x x/2-1=(3-x)/5

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