Solve for x (2x)/5=x+2

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

Step 1

Multiply both sides by $5$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x = (x + 2) \cdot 5$

Simplify the right side.

Simplify $(x + 2) \cdot 5$ .

Apply the distributive property.

$2 x = x \cdot 5 + 2 \cdot 5$

Simplify the expression.

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

$2 x = 5 \cdot x + 2 \cdot 5$

Multiply $2$ by $5$ .

$2 x = 5 x + 10$

Step 3

Solve for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$2 x - 5 x = 10$

Subtract $5 x$ from $2 x$ .

$- 3 x = 10$

Divide each term in $- 3 x = 10$ by $- 3$ and simplify.

Divide each term in $- 3 x = 10$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{10}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{10}{- 3}$

Divide $x$ by $1$ .

$x = \frac{10}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{10}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{10}{3}$

Decimal Form:

$x = - 3.\overline{3}$

Mixed Number Form:

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

Solve for x (2x)/5=x+2

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