Solve for x 6|6-4x|=8x+4

$6 | 6 - 4 x | = 8 x + 4$

Step 1

Divide each term in $6 | 6 - 4 x | = 8 x + 4$ by $6$ and simplify.

Divide each term in $6 | 6 - 4 x | = 8 x + 4$ by $6$ .

$\frac{6 | 6 - 4 x |}{6} = \frac{8 x}{6} + \frac{4}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 | 6 - 4 x |}{6} = \frac{8 x}{6} + \frac{4}{6}$

Divide $| 6 - 4 x |$ by $1$ .

$| 6 - 4 x | = \frac{8 x}{6} + \frac{4}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8 x$ .

$| 6 - 4 x | = \frac{2 (4 x)}{6} + \frac{4}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$| 6 - 4 x | = \frac{2 (4 x)}{2 (3)} + \frac{4}{6}$

Cancel the common factor.

$| 6 - 4 x | = \frac{2 (4 x)}{2 \cdot 3} + \frac{4}{6}$

Rewrite the expression.

$| 6 - 4 x | = \frac{4 x}{3} + \frac{4}{6}$

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$| 6 - 4 x | = \frac{4 x}{3} + \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$| 6 - 4 x | = \frac{4 x}{3} + \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$| 6 - 4 x | = \frac{4 x}{3} + \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$| 6 - 4 x | = \frac{4 x}{3} + \frac{2}{3}$

Step 2

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

$6 - 4 x = \pm (\frac{4 x}{3} + \frac{2}{3})$

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.

$6 - 4 x = \frac{4 x}{3} + \frac{2}{3}$

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

Subtract $\frac{4 x}{3}$ from both sides of the equation.

$6 - 4 x - \frac{4 x}{3} = \frac{2}{3}$

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 - 4 x \cdot \frac{3}{3} - \frac{4 x}{3} = \frac{2}{3}$

Combine $- 4 x$ and $\frac{3}{3}$ .

$6 + \frac{- 4 x \cdot 3}{3} - \frac{4 x}{3} = \frac{2}{3}$

Combine the numerators over the common denominator.

$6 + \frac{- 4 x \cdot 3 - 4 x}{3} = \frac{2}{3}$

Simplify each term.

Simplify the numerator.

Factor $4 x$ out of $- 4 x \cdot 3 - 4 x$ .

Factor $4 x$ out of $- 4 x \cdot 3$ .

$6 + \frac{4 x (- 1 \cdot 3) - 4 x}{3} = \frac{2}{3}$

Factor $4 x$ out of $- 4 x$ .

$6 + \frac{4 x (- 1 \cdot 3) + 4 x (- 1)}{3} = \frac{2}{3}$

Factor $4 x$ out of $4 x (- 1 \cdot 3) + 4 x (- 1)$ .

$6 + \frac{4 x (- 1 \cdot 3 - 1)}{3} = \frac{2}{3}$

Multiply $- 1$ by $3$ .

$6 + \frac{4 x (- 3 - 1)}{3} = \frac{2}{3}$

Subtract $1$ from $- 3$ .

$6 + \frac{4 x \cdot - 4}{3} = \frac{2}{3}$

Multiply $- 4$ by $4$ .

$6 + \frac{- 16 x}{3} = \frac{2}{3}$

Move the negative in front of the fraction.

$6 - \frac{16 x}{3} = \frac{2}{3}$

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

Subtract $6$ from both sides of the equation.

$- \frac{16 x}{3} = \frac{2}{3} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{16 x}{3} = \frac{2}{3} - 6 \cdot \frac{3}{3}$

Combine $- 6$ and $\frac{3}{3}$ .

$- \frac{16 x}{3} = \frac{2}{3} + \frac{- 6 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- \frac{16 x}{3} = \frac{2 - 6 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 6$ by $3$ .

$- \frac{16 x}{3} = \frac{2 - 18}{3}$

Subtract $18$ from $2$ .

$- \frac{16 x}{3} = \frac{- 16}{3}$

Move the negative in front of the fraction.

$- \frac{16 x}{3} = - \frac{16}{3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 16 x = - 16$

Divide each term in $- 16 x = - 16$ by $- 16$ and simplify.

Divide each term in $- 16 x = - 16$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{- 16}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{- 16}{- 16}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 16}$

Simplify the right side.

Divide $- 16$ by $- 16$ .

$x = 1$

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

$6 - 4 x = - (\frac{4 x}{3} + \frac{2}{3})$

Simplify $- (\frac{4 x}{3} + \frac{2}{3})$ .

Rewrite.

$6 - 4 x = 0 + 0 - (\frac{4 x}{3} + \frac{2}{3})$

Simplify by adding zeros.

$6 - 4 x = - (\frac{4 x}{3} + \frac{2}{3})$

Apply the distributive property.

$6 - 4 x = - \frac{4 x}{3} - \frac{2}{3}$

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

Add $\frac{4 x}{3}$ to both sides of the equation.

$6 - 4 x + \frac{4 x}{3} = - \frac{2}{3}$

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 - 4 x \cdot \frac{3}{3} + \frac{4 x}{3} = - \frac{2}{3}$

Combine $- 4 x$ and $\frac{3}{3}$ .

$6 + \frac{- 4 x \cdot 3}{3} + \frac{4 x}{3} = - \frac{2}{3}$

Combine the numerators over the common denominator.

$6 + \frac{- 4 x \cdot 3 + 4 x}{3} = - \frac{2}{3}$

Simplify each term.

Simplify the numerator.

Factor $4 x$ out of $- 4 x \cdot 3 + 4 x$ .

Factor $4 x$ out of $- 4 x \cdot 3$ .

$6 + \frac{4 x (- 1 \cdot 3) + 4 x}{3} = - \frac{2}{3}$

Factor $4 x$ out of $4 x$ .

$6 + \frac{4 x (- 1 \cdot 3) + 4 x (1)}{3} = - \frac{2}{3}$

Factor $4 x$ out of $4 x (- 1 \cdot 3) + 4 x (1)$ .

$6 + \frac{4 x (- 1 \cdot 3 + 1)}{3} = - \frac{2}{3}$

Multiply $- 1$ by $3$ .

$6 + \frac{4 x (- 3 + 1)}{3} = - \frac{2}{3}$

Add $- 3$ and $1$ .

$6 + \frac{4 x \cdot - 2}{3} = - \frac{2}{3}$

Multiply $- 2$ by $4$ .

$6 + \frac{- 8 x}{3} = - \frac{2}{3}$

Move the negative in front of the fraction.

$6 - \frac{8 x}{3} = - \frac{2}{3}$

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

Subtract $6$ from both sides of the equation.

$- \frac{8 x}{3} = - \frac{2}{3} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{8 x}{3} = - \frac{2}{3} - 6 \cdot \frac{3}{3}$

Combine $- 6$ and $\frac{3}{3}$ .

$- \frac{8 x}{3} = - \frac{2}{3} + \frac{- 6 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- \frac{8 x}{3} = \frac{- 2 - 6 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 6$ by $3$ .

$- \frac{8 x}{3} = \frac{- 2 - 18}{3}$

Subtract $18$ from $- 2$ .

$- \frac{8 x}{3} = \frac{- 20}{3}$

Move the negative in front of the fraction.

$- \frac{8 x}{3} = - \frac{20}{3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 8 x = - 20$

Divide each term in $- 8 x = - 20$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 20$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 20}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 20}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 20}{- 8}$

Simplify the right side.

Cancel the common factor of $- 20$ and $- 8$ .

Factor $- 4$ out of $- 20$ .

$x = \frac{- 4 (5)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

$x = \frac{- 4 \cdot 5}{- 4 \cdot 2}$

Cancel the common factor.

$x = \frac{- 4 \cdot 5}{- 4 \cdot 2}$

Rewrite the expression.

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

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

$x = 1, \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 1, \frac{5}{2}$

Decimal Form:

$x = 1, 2.5$

Mixed Number Form:

$x = 1, 2 \frac{1}{2}$

Solve for x 6|6-4x|=8x+4

Related Questions

Support LCMGCF.com by disabling your adblocker.