Solve for x a/3=2/5x-1

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

Step 1

Rewrite the equation as $\frac{2}{5} x - 1 = \frac{a}{3}$ .

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

Step 2

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

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

Step 3

Add $1$ to both sides of the equation.

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

Step 4

Multiply both sides of the equation by $\frac{5}{2}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{2} \cdot \frac{2 x}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{5}{2} (\frac{a}{3} + 1)$ .

Apply the distributive property.

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

Multiply $\frac{5}{2} \cdot \frac{a}{3}$ .

Multiply $\frac{5}{2}$ by $\frac{a}{3}$ .

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

Multiply $2$ by $3$ .

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

Multiply $\frac{5}{2}$ by $1$ .

$x = \frac{5 a}{6} + \frac{5}{2}$