Solve for x 3(9x+2)+21x=1/2(6x-8)+75x

$3 (9 x + 2) + 21 x = \frac{1}{2} (6 x - 8) + 75 x$

Simplify $3 (9 x + 2) + 21 x$ .

Simplify each term.

Apply the distributive property.

$3 (9 x) + 3 \cdot 2 + 21 x = \frac{1}{2} \cdot (6 x - 8) + 75 x$

Multiply $9$ by $3$ .

$27 x + 3 \cdot 2 + 21 x = \frac{1}{2} \cdot (6 x - 8) + 75 x$

Multiply $3$ by $2$ .

$27 x + 6 + 21 x = \frac{1}{2} \cdot (6 x - 8) + 75 x$

Add $27 x$ and $21 x$ .

$48 x + 6 = \frac{1}{2} \cdot (6 x - 8) + 75 x$

Simplify $\frac{1}{2} \cdot (6 x - 8) + 75 x$ .

Simplify each term.

Apply the distributive property.

$48 x + 6 = \frac{1}{2} (6 x) + \frac{1}{2} \cdot - 8 + 75 x$

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

$48 x + 6 = \frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 8 + 75 x$

Cancel the common factor.

$48 x + 6 = \frac{1}{2} (2 (3 x)) + \frac{1}{2} \cdot - 8 + 75 x$

Rewrite the expression.

$48 x + 6 = 3 x + \frac{1}{2} \cdot - 8 + 75 x$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$48 x + 6 = 3 x + \frac{1}{2} \cdot (2 (- 4)) + 75 x$

Cancel the common factor.

$48 x + 6 = 3 x + \frac{1}{2} \cdot (2 \cdot - 4) + 75 x$

Rewrite the expression.

$48 x + 6 = 3 x - 4 + 75 x$

Add $3 x$ and $75 x$ .

$48 x + 6 = 78 x - 4$

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

Subtract $78 x$ from both sides of the equation.

$48 x + 6 - 78 x = - 4$

Subtract $78 x$ from $48 x$ .

$- 30 x + 6 = - 4$

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

Subtract $6$ from both sides of the equation.

$- 30 x = - 4 - 6$

Subtract $6$ from $- 4$ .

$- 30 x = - 10$

Divide each term in $- 30 x = - 10$ by $- 30$ and simplify.

Divide each term in $- 30 x = - 10$ by $- 30$ .

$\frac{- 30 x}{- 30} = \frac{- 10}{- 30}$

Simplify the left side.

Cancel the common factor of $- 30$ .

Cancel the common factor.

$\frac{- 30 x}{- 30} = \frac{- 10}{- 30}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 30}$

Simplify the right side.

Cancel the common factor of $- 10$ and $- 30$ .

Factor $- 10$ out of $- 10$ .

$x = \frac{- 10 (1)}{- 30}$

Cancel the common factors.

Factor $- 10$ out of $- 30$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$

Solve for x 3(9x+2)+21x=1/2(6x-8)+75x

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