Solve for x 1/3(6x+30)=4x+2(x-7)

$\frac{1}{3} (6 x + 30) = 4 x + 2 (x - 7)$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x + 2 (x - 7) = \frac{1}{3} \cdot (6 x + 30)$

Simplify $4 x + 2 (x - 7)$ .

Simplify each term.

Apply the distributive property.

$4 x + 2 x + 2 \cdot - 7 = \frac{1}{3} \cdot (6 x + 30)$

Multiply $2$ by $- 7$ .

$4 x + 2 x - 14 = \frac{1}{3} \cdot (6 x + 30)$

Add $4 x$ and $2 x$ .

$6 x - 14 = \frac{1}{3} \cdot (6 x + 30)$

Simplify $\frac{1}{3} \cdot (6 x + 30)$ .

Apply the distributive property.

$6 x - 14 = \frac{1}{3} (6 x) + \frac{1}{3} \cdot 30$

Cancel the common factor of $3$ .

Factor $3$ out of $6 x$ .

$6 x - 14 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot 30$

Cancel the common factor.

$6 x - 14 = \frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot 30$

Rewrite the expression.

$6 x - 14 = 2 x + \frac{1}{3} \cdot 30$

Cancel the common factor of $3$ .

Factor $3$ out of $30$ .

$6 x - 14 = 2 x + \frac{1}{3} \cdot (3 (10))$

Cancel the common factor.

$6 x - 14 = 2 x + \frac{1}{3} \cdot (3 \cdot 10)$

Rewrite the expression.

$6 x - 14 = 2 x + 10$

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

Subtract $2 x$ from both sides of the equation.

$6 x - 14 - 2 x = 10$

Subtract $2 x$ from $6 x$ .

$4 x - 14 = 10$

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

Add $14$ to both sides of the equation.

$4 x = 10 + 14$

Add $10$ and $14$ .

$4 x = 24$

Divide each term in $4 x = 24$ by $4$ and simplify.

Divide each term in $4 x = 24$ by $4$ .

$\frac{4 x}{4} = \frac{24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{24}{4}$

Divide $x$ by $1$ .

$x = \frac{24}{4}$

Simplify the right side.

Divide $24$ by $4$ .

$x = 6$

Solve for x 1/3(6x+30)=4x+2(x-7)

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