Solve for x -x=10(6/5x-6/5)+1/2x

$- x = 10 (\frac{6}{5} x - \frac{6}{5}) + \frac{1}{2} x$

Step 1

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

$10 (\frac{6}{5} x - \frac{6}{5}) + \frac{1}{2} x = - x$

Step 2

Simplify $10 (\frac{6}{5} x - \frac{6}{5}) + \frac{1}{2} x$ .

Simplify each term.

Combine $\frac{6}{5}$ and $x$ .

$10 (\frac{6 x}{5} - \frac{6}{5}) + \frac{1}{2} x = - x$

Apply the distributive property.

$10 \frac{6 x}{5} + 10 (- \frac{6}{5}) + \frac{1}{2} x = - x$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$5 (2) \frac{6 x}{5} + 10 (- \frac{6}{5}) + \frac{1}{2} x = - x$

Cancel the common factor.

$5 \cdot 2 \frac{6 x}{5} + 10 (- \frac{6}{5}) + \frac{1}{2} x = - x$

Rewrite the expression.

$2 (6 x) + 10 (- \frac{6}{5}) + \frac{1}{2} x = - x$

Multiply $6$ by $2$ .

$12 x + 10 (- \frac{6}{5}) + \frac{1}{2} x = - x$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$12 x + 10 (\frac{- 6}{5}) + \frac{1}{2} x = - x$

Factor $5$ out of $10$ .

$12 x + 5 (2) \frac{- 6}{5} + \frac{1}{2} x = - x$

Cancel the common factor.

$12 x + 5 \cdot 2 \frac{- 6}{5} + \frac{1}{2} x = - x$

Rewrite the expression.

$12 x + 2 \cdot - 6 + \frac{1}{2} x = - x$

Multiply $2$ by $- 6$ .

$12 x - 12 + \frac{1}{2} x = - x$

Combine $\frac{1}{2}$ and $x$ .

$12 x - 12 + \frac{x}{2} = - x$

To write $12 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$12 x \cdot \frac{2}{2} + \frac{x}{2} - 12 = - x$

Simplify terms.

Combine $12 x$ and $\frac{2}{2}$ .

$\frac{12 x \cdot 2}{2} + \frac{x}{2} - 12 = - x$

Combine the numerators over the common denominator.

$\frac{12 x \cdot 2 + x}{2} - 12 = - x$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $12 x \cdot 2 + x$ .

Factor $x$ out of $12 x \cdot 2$ .

$\frac{x (12 \cdot 2) + x}{2} - 12 = - x$

Raise $x$ to the power of $1$ .

$\frac{x (12 \cdot 2) + x^{1}}{2} - 12 = - x$

Factor $x$ out of $x^{1}$ .

$\frac{x (12 \cdot 2) + x \cdot 1}{2} - 12 = - x$

Factor $x$ out of $x (12 \cdot 2) + x \cdot 1$ .

$\frac{x (12 \cdot 2 + 1)}{2} - 12 = - x$

Multiply $12$ by $2$ .

$\frac{x (24 + 1)}{2} - 12 = - x$

Add $24$ and $1$ .

$\frac{x \cdot 25}{2} - 12 = - x$

Move $25$ to the left of $x$ .

$\frac{25 x}{2} - 12 = - x$

Step 3

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

Add $x$ to both sides of the equation.

$\frac{25 x}{2} - 12 + x = 0$

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25 x}{2} + x \cdot \frac{2}{2} - 12 = 0$

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

$\frac{25 x}{2} + \frac{x \cdot 2}{2} - 12 = 0$

Combine the numerators over the common denominator.

$\frac{25 x + x \cdot 2}{2} - 12 = 0$

Add $25 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

$\frac{25 x + 2 \cdot x}{2} - 12 = 0$

Add $25 x$ and $2 \cdot x$ .

$\frac{27 x}{2} - 12 = 0$

Step 4

Add $12$ to both sides of the equation.

$\frac{27 x}{2} = 12$

Step 5

Multiply both sides of the equation by $\frac{2}{27}$ .

$\frac{2}{27} \cdot \frac{27 x}{2} = \frac{2}{27} \cdot 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{27} \cdot \frac{27 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{27} \cdot \frac{27 x}{2} = \frac{2}{27} \cdot 12$

Rewrite the expression.

$\frac{1}{27} (27 x) = \frac{2}{27} \cdot 12$

Cancel the common factor of $27$ .

Factor $27$ out of $27 x$ .

$\frac{1}{27} (27 (x)) = \frac{2}{27} \cdot 12$

Cancel the common factor.

$\frac{1}{27} (27 x) = \frac{2}{27} \cdot 12$

Rewrite the expression.

$x = \frac{2}{27} \cdot 12$

Simplify the right side.

Simplify $\frac{2}{27} \cdot 12$ .

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$x = \frac{2}{3 (9)} \cdot 12$

Factor $3$ out of $12$ .

$x = \frac{2}{3 \cdot 9} \cdot (3 \cdot 4)$

Cancel the common factor.

$x = \frac{2}{3 \cdot 9} \cdot (3 \cdot 4)$

Rewrite the expression.

$x = \frac{2}{9} \cdot 4$

Combine $\frac{2}{9}$ and $4$ .

$x = \frac{2 \cdot 4}{9}$

Multiply $2$ by $4$ .

$x = \frac{8}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{9}$

Decimal Form:

$x = 0.\overline{8}$

Solve for x -x=10(6/5x-6/5)+1/2x

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