Solve for a |(3-5a)/4|-1/3=2/3

$| \frac{3 - 5 a}{4} | - \frac{1}{3} = \frac{2}{3}$

Step 1

Move all terms not containing $| \frac{3 - 5 a}{4} |$ to the right side of the equation.

Add $\frac{1}{3}$ to both sides of the equation.

$| \frac{3 - 5 a}{4} | = \frac{2}{3} + \frac{1}{3}$

Combine the numerators over the common denominator.

$| \frac{3 - 5 a}{4} | = \frac{2 + 1}{3}$

Add $2$ and $1$ .

$| \frac{3 - 5 a}{4} | = \frac{3}{3}$

Divide $3$ by $3$ .

$| \frac{3 - 5 a}{4} | = 1$

Step 2

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

$\frac{3 - 5 a}{4} = \pm 1$

Step 3

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.

$\frac{3 - 5 a}{4} = 1$

Multiply both sides by $4$ .

$\frac{3 - 5 a}{4} \cdot 4 = 1 \cdot 4$

Simplify.

Simplify the left side.

Simplify $\frac{3 - 5 a}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 - 5 a}{4} \cdot 4 = 1 \cdot 4$

Rewrite the expression.

$3 - 5 a = 1 \cdot 4$

Reorder $3$ and $- 5 a$ .

$- 5 a + 3 = 1 \cdot 4$

Simplify the right side.

Multiply $4$ by $1$ .

$- 5 a + 3 = 4$

Solve for $a$ .

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

Subtract $3$ from both sides of the equation.

$- 5 a = 4 - 3$

Subtract $3$ from $4$ .

$- 5 a = 1$

Divide each term in $- 5 a = 1$ by $- 5$ and simplify.

Divide each term in $- 5 a = 1$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{1}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{1}{- 5}$

Divide $a$ by $1$ .

$a = \frac{1}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{1}{5}$

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

$\frac{3 - 5 a}{4} = - 1$

Multiply both sides by $4$ .

$\frac{3 - 5 a}{4} \cdot 4 = - 1 \cdot 4$

Simplify.

Simplify the left side.

Simplify $\frac{3 - 5 a}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 - 5 a}{4} \cdot 4 = - 1 \cdot 4$

Rewrite the expression.

$3 - 5 a = - 1 \cdot 4$

Reorder $3$ and $- 5 a$ .

$- 5 a + 3 = - 1 \cdot 4$

Simplify the right side.

Multiply $- 1$ by $4$ .

$- 5 a + 3 = - 4$

Solve for $a$ .

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

Subtract $3$ from both sides of the equation.

$- 5 a = - 4 - 3$

Subtract $3$ from $- 4$ .

$- 5 a = - 7$

Divide each term in $- 5 a = - 7$ by $- 5$ and simplify.

Divide each term in $- 5 a = - 7$ by $- 5$ .

$\frac{- 5 a}{- 5} = \frac{- 7}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 a}{- 5} = \frac{- 7}{- 5}$

Divide $a$ by $1$ .

$a = \frac{- 7}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$a = \frac{7}{5}$

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

$a = - \frac{1}{5}, \frac{7}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{1}{5}, \frac{7}{5}$

Decimal Form:

$a = - 0.2, 1.4$

Mixed Number Form:

$a = - \frac{1}{5}, 1 \frac{2}{5}$

Solve for a |(3-5a)/4|-1/3=2/3

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