Algebra Examples

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

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.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

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

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

Step 2.1.3.2

Factor $2$ out of $- 6$ .

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

Step 2.1.3.3

Cancel the common factor.

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

Step 2.1.3.4

Rewrite the expression.

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

Step 2.1.4

Multiply $- 3$ by $- 3$ .

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

Step 2.1.5

Cancel the common factor of $6$ .

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Step 2.1.5.1

Factor $6$ out of $- 6$ .

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

Step 2.1.5.2

Cancel the common factor.

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

Step 2.1.5.3

Rewrite the expression.

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $x$ and $9 x$ .

$10 x - 1 - 1 = 7 x$

Step 2.2.2

Subtract $1$ from $- 1$ .

$10 x - 2 = 7 x$

Step 3

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

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Step 3.1

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

$10 x - 2 - 7 x = 0$

Step 3.2

Subtract $7 x$ from $10 x$ .

$3 x - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$3 x = 2$

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$