Solve for x (4-2x)/3=7x+4

$\frac{4 - 2 x}{3} = 7 x + 4$

Step 1

Multiply both sides by $3$ .

$\frac{4 - 2 x}{3} \cdot 3 = (7 x + 4) \cdot 3$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{4 - 2 x}{3} \cdot 3$ .

Factor $2$ out of $4 - 2 x$ .

Factor $2$ out of $4$ .

$\frac{2 (2) - 2 x}{3} \cdot 3 = (7 x + 4) \cdot 3$

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

$\frac{2 (2) + 2 (- x)}{3} \cdot 3 = (7 x + 4) \cdot 3$

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

$\frac{2 (2 - x)}{3} \cdot 3 = (7 x + 4) \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 (2 - x)}{3} \cdot 3 = (7 x + 4) \cdot 3$

Rewrite the expression.

$2 (2 - x) = (7 x + 4) \cdot 3$

Apply the distributive property.

$2 \cdot 2 + 2 (- x) = (7 x + 4) \cdot 3$

Simplify the expression.

Multiply $2$ by $2$ .

$4 + 2 (- x) = (7 x + 4) \cdot 3$

Multiply $- 1$ by $2$ .

$4 - 2 x = (7 x + 4) \cdot 3$

Reorder $4$ and $- 2 x$ .

$- 2 x + 4 = (7 x + 4) \cdot 3$

Simplify the right side.

Simplify $(7 x + 4) \cdot 3$ .

Apply the distributive property.

$- 2 x + 4 = 7 x \cdot 3 + 4 \cdot 3$

Multiply.

Multiply $3$ by $7$ .

$- 2 x + 4 = 21 x + 4 \cdot 3$

Multiply $4$ by $3$ .

$- 2 x + 4 = 21 x + 12$

Step 3

Solve for $x$ .

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

Subtract $21 x$ from both sides of the equation.

$- 2 x + 4 - 21 x = 12$

Subtract $21 x$ from $- 2 x$ .

$- 23 x + 4 = 12$

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

Subtract $4$ from both sides of the equation.

$- 23 x = 12 - 4$

Subtract $4$ from $12$ .

$- 23 x = 8$

Divide each term in $- 23 x = 8$ by $- 23$ and simplify.

Divide each term in $- 23 x = 8$ by $- 23$ .

$\frac{- 23 x}{- 23} = \frac{8}{- 23}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 x}{- 23} = \frac{8}{- 23}$

Divide $x$ by $1$ .

$x = \frac{8}{- 23}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{23}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{23}$

Decimal Form:

$x = - 0.34782608 \dots$

Solve for x (4-2x)/3=7x+4

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