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

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

Step 1

Simplify $3 (x - 2) + 7 x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

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

Add $3 x$ and $7 x$ .

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

Step 2

Simplify $\frac{1}{2} \cdot (6 x - 2)$ .

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$10 x - 6 = 3 x - 1$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$10 x - 6 - 3 x = - 1$

Subtract $3 x$ from $10 x$ .

$7 x - 6 = - 1$

Step 4

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

Add $6$ to both sides of the equation.

$7 x = - 1 + 6$

Add $- 1$ and $6$ .

$7 x = 5$

Step 5

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

Divide each term in $7 x = 5$ by $7$ .

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{714285}$

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

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