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

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

Step 1

Simplify $\frac{x}{5} + \frac{2 x}{3} + x$ .

Find the common denominator.

Multiply $\frac{x}{5}$ by $\frac{3}{3}$ .

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

Multiply $\frac{x}{5}$ by $\frac{3}{3}$ .

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

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

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

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

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

Write $x$ as a fraction with denominator $1$ .

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

Multiply $\frac{x}{1}$ by $\frac{15}{15}$ .

$\frac{x \cdot 3}{5 \cdot 3} + \frac{2 x \cdot 5}{3 \cdot 5} + \frac{x}{1} \cdot \frac{15}{15} = 2$

Multiply $\frac{x}{1}$ by $\frac{15}{15}$ .

$\frac{x \cdot 3}{5 \cdot 3} + \frac{2 x \cdot 5}{3 \cdot 5} + \frac{x \cdot 15}{15} = 2$

Reorder the factors of $5 \cdot 3$ .

$\frac{x \cdot 3}{3 \cdot 5} + \frac{2 x \cdot 5}{3 \cdot 5} + \frac{x \cdot 15}{15} = 2$

Multiply $3$ by $5$ .

$\frac{x \cdot 3}{15} + \frac{2 x \cdot 5}{3 \cdot 5} + \frac{x \cdot 15}{15} = 2$

Multiply $3$ by $5$ .

$\frac{x \cdot 3}{15} + \frac{2 x \cdot 5}{15} + \frac{x \cdot 15}{15} = 2$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + 2 x \cdot 5 + x \cdot 15}{15} = 2$

Simplify each term.

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 2 x \cdot 5 + x \cdot 15}{15} = 2$

Multiply $5$ by $2$ .

$\frac{3 x + 10 x + x \cdot 15}{15} = 2$

Move $15$ to the left of $x$ .

$\frac{3 x + 10 x + 15 x}{15} = 2$

Simplify by adding terms.

Add $3 x$ and $10 x$ .

$\frac{13 x + 15 x}{15} = 2$

Add $13 x$ and $15 x$ .

$\frac{28 x}{15} = 2$

Step 2

Multiply both sides of the equation by $\frac{15}{28}$ .

$\frac{15}{28} \cdot \frac{28 x}{15} = \frac{15}{28} \cdot 2$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{15}{28} \cdot \frac{28 x}{15}$ .

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15}{28} \cdot \frac{28 x}{15} = \frac{15}{28} \cdot 2$

Rewrite the expression.

$\frac{1}{28} (28 x) = \frac{15}{28} \cdot 2$

Cancel the common factor of $28$ .

Factor $28$ out of $28 x$ .

$\frac{1}{28} (28 (x)) = \frac{15}{28} \cdot 2$

Cancel the common factor.

$\frac{1}{28} (28 x) = \frac{15}{28} \cdot 2$

Rewrite the expression.

$x = \frac{15}{28} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $28$ .

$x = \frac{15}{2 (14)} \cdot 2$

Cancel the common factor.

$x = \frac{15}{2 \cdot 14} \cdot 2$

Rewrite the expression.

$x = \frac{15}{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{14}$

Decimal Form:

$x = 1.07142857 \dots$

Mixed Number Form:

$x = 1 \frac{1}{14}$

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

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