Solve for x |(3-7x)/9|=3/5

$| \frac{3 - 7 x}{9} | = \frac{3}{5}$

Step 1

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

$\frac{3 - 7 x}{9} = \pm \frac{3}{5}$

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.

$\frac{3 - 7 x}{9} = \frac{3}{5}$

Multiply both sides by $9$ .

$\frac{3 - 7 x}{9} \cdot 9 = \frac{3}{5} \cdot 9$

Simplify.

Simplify the left side.

Simplify $\frac{3 - 7 x}{9} \cdot 9$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{3 - 7 x}{9} \cdot 9 = \frac{3}{5} \cdot 9$

Rewrite the expression.

$3 - 7 x = \frac{3}{5} \cdot 9$

Reorder $3$ and $- 7 x$ .

$- 7 x + 3 = \frac{3}{5} \cdot 9$

Simplify the right side.

Multiply $\frac{3}{5} \cdot 9$ .

Combine $\frac{3}{5}$ and $9$ .

$- 7 x + 3 = \frac{3 \cdot 9}{5}$

Multiply $3$ by $9$ .

$- 7 x + 3 = \frac{27}{5}$

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$- 7 x = \frac{27}{5} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 7 x = \frac{27}{5} - 3 \cdot \frac{5}{5}$

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

$- 7 x = \frac{27}{5} + \frac{- 3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$- 7 x = \frac{27 - 3 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$- 7 x = \frac{27 - 15}{5}$

Subtract $15$ from $27$ .

$- 7 x = \frac{12}{5}$

Divide each term in $- 7 x = \frac{12}{5}$ by $- 7$ and simplify.

Divide each term in $- 7 x = \frac{12}{5}$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{\frac{12}{5}}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{\frac{12}{5}}{- 7}$

Divide $x$ by $1$ .

$x = \frac{\frac{12}{5}}{- 7}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{12}{5} \cdot \frac{1}{- 7}$

Move the negative in front of the fraction.

$x = \frac{12}{5} (- \frac{1}{7})$

Multiply $\frac{12}{5} (- \frac{1}{7})$ .

Multiply $\frac{12}{5}$ by $\frac{1}{7}$ .

$x = - \frac{12}{5 \cdot 7}$

Multiply $5$ by $7$ .

$x = - \frac{12}{35}$

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

$\frac{3 - 7 x}{9} = - \frac{3}{5}$

Multiply both sides by $9$ .

$\frac{3 - 7 x}{9} \cdot 9 = - \frac{3}{5} \cdot 9$

Simplify.

Simplify the left side.

Simplify $\frac{3 - 7 x}{9} \cdot 9$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{3 - 7 x}{9} \cdot 9 = - \frac{3}{5} \cdot 9$

Rewrite the expression.

$3 - 7 x = - \frac{3}{5} \cdot 9$

Reorder $3$ and $- 7 x$ .

$- 7 x + 3 = - \frac{3}{5} \cdot 9$

Simplify the right side.

Simplify $- \frac{3}{5} \cdot 9$ .

Multiply $- \frac{3}{5} \cdot 9$ .

Multiply $9$ by $- 1$ .

$- 7 x + 3 = - 9 (\frac{3}{5})$

Combine $- 9$ and $\frac{3}{5}$ .

$- 7 x + 3 = \frac{- 9 \cdot 3}{5}$

Multiply $- 9$ by $3$ .

$- 7 x + 3 = \frac{- 27}{5}$

Move the negative in front of the fraction.

$- 7 x + 3 = - \frac{27}{5}$

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$- 7 x = - \frac{27}{5} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 7 x = - \frac{27}{5} - 3 \cdot \frac{5}{5}$

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

$- 7 x = - \frac{27}{5} + \frac{- 3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$- 7 x = \frac{- 27 - 3 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$- 7 x = \frac{- 27 - 15}{5}$

Subtract $15$ from $- 27$ .

$- 7 x = \frac{- 42}{5}$

Move the negative in front of the fraction.

$- 7 x = - \frac{42}{5}$

Divide each term in $- 7 x = - \frac{42}{5}$ by $- 7$ and simplify.

Divide each term in $- 7 x = - \frac{42}{5}$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- \frac{42}{5}}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- \frac{42}{5}}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- \frac{42}{5}}{- 7}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{42}{5} \cdot \frac{1}{- 7}$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{42}{5}$ into the numerator.

$x = \frac{- 42}{5} \cdot \frac{1}{- 7}$

Factor $7$ out of $- 42$ .

$x = \frac{7 (- 6)}{5} \cdot \frac{1}{- 7}$

Factor $7$ out of $- 7$ .

$x = \frac{7 \cdot - 6}{5} \cdot \frac{1}{7 \cdot - 1}$

Cancel the common factor.

$x = \frac{7 \cdot - 6}{5} \cdot \frac{1}{7 \cdot - 1}$

Rewrite the expression.

$x = \frac{- 6}{5} \cdot \frac{1}{- 1}$

Multiply $\frac{- 6}{5}$ by $\frac{1}{- 1}$ .

$x = \frac{- 6}{5 \cdot - 1}$

Multiply $5$ by $- 1$ .

$x = \frac{- 6}{- 5}$

Dividing two negative values results in a positive value.

$x = \frac{6}{5}$

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

$x = - \frac{12}{35}, \frac{6}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{35}, \frac{6}{5}$

Decimal Form:

$x = - 0.3\overline{428571}, 1.2$

Mixed Number Form:

$x = - \frac{12}{35}, 1 \frac{1}{5}$

Solve for x |(3-7x)/9|=3/5

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