Solve for x 4/6x-4x+8/3=4/3

$\frac{4}{6} x - 4 x + \frac{8}{3} = \frac{4}{3}$

Step 1

Simplify $\frac{4}{6} x - 4 x + \frac{8}{3}$ .

Simplify each term.

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

Factor $2$ out of $4$ .

$\frac{2 (2)}{6} x - 4 x + \frac{8}{3} = \frac{4}{3}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 \cdot 2}{2 \cdot 3} x - 4 x + \frac{8}{3} = \frac{4}{3}$

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 3} x - 4 x + \frac{8}{3} = \frac{4}{3}$

Rewrite the expression.

$\frac{2}{3} x - 4 x + \frac{8}{3} = \frac{4}{3}$

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} - 4 x + \frac{8}{3} = \frac{4}{3}$

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

$\frac{2 x}{3} - 4 x \cdot \frac{3}{3} + \frac{8}{3} = \frac{4}{3}$

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

$\frac{2 x}{3} + \frac{- 4 x \cdot 3}{3} + \frac{8}{3} = \frac{4}{3}$

Combine the numerators over the common denominator.

$\frac{2 x - 4 x \cdot 3}{3} + \frac{8}{3} = \frac{4}{3}$

Combine the numerators over the common denominator.

$\frac{2 x - 4 x \cdot 3 + 8}{3} = \frac{4}{3}$

Multiply $3$ by $- 4$ .

$\frac{2 x - 12 x + 8}{3} = \frac{4}{3}$

Subtract $12 x$ from $2 x$ .

$\frac{- 10 x + 8}{3} = \frac{4}{3}$

Factor $2$ out of $- 10 x + 8$ .

Factor $2$ out of $- 10 x$ .

$\frac{2 (- 5 x) + 8}{3} = \frac{4}{3}$

Factor $2$ out of $8$ .

$\frac{2 (- 5 x) + 2 (4)}{3} = \frac{4}{3}$

Factor $2$ out of $2 (- 5 x) + 2 (4)$ .

$\frac{2 (- 5 x + 4)}{3} = \frac{4}{3}$

Factor $- 1$ out of $- 5 x$ .

$\frac{2 (- (5 x) + 4)}{3} = \frac{4}{3}$

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{2 (- (5 x) - 1 (- 4))}{3} = \frac{4}{3}$

Factor $- 1$ out of $- (5 x) - 1 (- 4)$ .

$\frac{2 (- (5 x - 4))}{3} = \frac{4}{3}$

Simplify the expression.

Rewrite $- (5 x - 4)$ as $- 1 (5 x - 4)$ .

$\frac{2 (- 1 (5 x - 4))}{3} = \frac{4}{3}$

Move the negative in front of the fraction.

$- \frac{2 (5 x - 4)}{3} = \frac{4}{3}$

Step 2

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

$- 2 (5 x - 4) = 4$

Step 3

Divide each term in $- 2 (5 x - 4) = 4$ by $- 2$ and simplify.

Divide each term in $- 2 (5 x - 4) = 4$ by $- 2$ .

$\frac{- 2 (5 x - 4)}{- 2} = \frac{4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (5 x - 4)}{- 2} = \frac{4}{- 2}$

Divide $5 x - 4$ by $1$ .

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

Simplify the right side.

Divide $4$ by $- 2$ .

$5 x - 4 = - 2$

Step 4

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

Add $4$ to both sides of the equation.

$5 x = - 2 + 4$

Add $- 2$ and $4$ .

$5 x = 2$

Step 5

Divide each term in $5 x = 2$ by $5$ and simplify.

Divide each term in $5 x = 2$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.4$

Solve for x 4/6x-4x+8/3=4/3

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