Algebra Examples

$\frac{1}{3} (9 - 6 x) = - 4 x$

Step 1

Simplify $\frac{1}{3} \cdot (9 - 6 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (9 - 6 x) = - 4 x$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (9 - 6 x) = - 4 x$

Step 1.3

Apply the distributive property.

$\frac{1}{3} \cdot 9 + \frac{1}{3} (- 6 x) = - 4 x$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

$3 + \frac{1}{3} (- 6 x) = - 4 x$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 6 x$ .

$3 + \frac{1}{3} (3 (- 2 x)) = - 4 x$

Step 1.5.2

Cancel the common factor.

$3 + \frac{1}{3} (3 (- 2 x)) = - 4 x$

Step 1.5.3

Rewrite the expression.

$3 - 2 x = - 4 x$

Step 2

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

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Step 2.1

Add $4 x$ to both sides of the equation.

$3 - 2 x + 4 x = 0$

Step 2.2

Add $- 2 x$ and $4 x$ .

$3 + 2 x = 0$

Step 3

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

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