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

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

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

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

Simplify $x - 6 (- \frac{3}{2} x + \frac{1}{6}) - 1$ .

Simplify each term.

Combine $x$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $x$ .

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

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

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 3$ by $- 3$ .

$x + 9 x - 6 (\frac{1}{6}) - 1 = 7 x$

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$x + 9 x + 6 (- 1) \frac{1}{6} - 1 = 7 x$

Cancel the common factor.

$x + 9 x + 6 \cdot - 1 \frac{1}{6} - 1 = 7 x$

Rewrite the expression.

$x + 9 x - 1 - 1 = 7 x$

Simplify by adding terms.

Add $x$ and $9 x$ .

$10 x - 1 - 1 = 7 x$

Subtract $1$ from $- 1$ .

$10 x - 2 = 7 x$

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

Subtract $7 x$ from both sides of the equation.

$10 x - 2 - 7 x = 0$

Subtract $7 x$ from $10 x$ .

$3 x - 2 = 0$

Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$

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

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