Solve for x |x/3+2/5|=2

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

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

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

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

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

Subtract $\frac{2}{5}$ from both sides of the equation.

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $5$ .

$\frac{x}{3} = \frac{10 - 2}{5}$

Subtract $2$ from $10$ .

$\frac{x}{3} = \frac{8}{5}$

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (\frac{8}{5})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 (\frac{8}{5})$

Rewrite the expression.

$x = 3 (\frac{8}{5})$

Simplify the right side.

Multiply $3 (\frac{8}{5})$ .

Combine $3$ and $\frac{8}{5}$ .

$x = \frac{3 \cdot 8}{5}$

Multiply $3$ by $8$ .

$x = \frac{24}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

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

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

Subtract $\frac{2}{5}$ from both sides of the equation.

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $5$ .

$\frac{x}{3} = \frac{- 10 - 2}{5}$

Subtract $2$ from $- 10$ .

$\frac{x}{3} = \frac{- 12}{5}$

Move the negative in front of the fraction.

$\frac{x}{3} = - \frac{12}{5}$

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (- \frac{12}{5})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 (- \frac{12}{5})$

Rewrite the expression.

$x = 3 (- \frac{12}{5})$

Simplify the right side.

Simplify $3 (- \frac{12}{5})$ .

Multiply $3 (- \frac{12}{5})$ .

Multiply $- 1$ by $3$ .

$x = - 3 (\frac{12}{5})$

Combine $- 3$ and $\frac{12}{5}$ .

$x = \frac{- 3 \cdot 12}{5}$

Multiply $- 3$ by $12$ .

$x = \frac{- 36}{5}$

Move the negative in front of the fraction.

$x = - \frac{36}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{24}{5}, - \frac{36}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{5}, - \frac{36}{5}$

Decimal Form:

$x = 4.8, - 7.2$

Mixed Number Form:

$x = 4 \frac{4}{5}, - 7 \frac{1}{5}$

Solve for x |x/3+2/5|=2

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