Algebra Examples

$4 x - \frac{1}{3} (15 x - 3 (- 1 + 2 x)) = \frac{3}{2} (9 - x - 6)$

Step 1

Simplify $4 x - \frac{1}{3} \cdot (15 x - 3 (- 1 + 2 x))$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$4 x - \frac{1}{3} \cdot (15 x - 3 \cdot - 1 - 3 (2 x)) = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.1.2

Multiply $- 3$ by $- 1$ .

$4 x - \frac{1}{3} \cdot (15 x + 3 - 3 (2 x)) = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.1.3

Multiply $2$ by $- 3$ .

$4 x - \frac{1}{3} \cdot (15 x + 3 - 6 x) = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.2

Subtract $6 x$ from $15 x$ .

$4 x - \frac{1}{3} \cdot (9 x + 3) = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.3

Apply the distributive property.

$4 x - \frac{1}{3} (9 x) - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$4 x + \frac{- 1}{3} (9 x) - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.4.2

Factor $3$ out of $9 x$ .

$4 x + \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.4.3

Cancel the common factor.

$4 x + \frac{- 1}{3} (3 (3 x)) - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.4.4

Rewrite the expression.

$4 x - 1 (3 x) - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.5

Multiply $3$ by $- 1$ .

$4 x - 3 x - \frac{1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.6

Cancel the common factor of $3$ .

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Step 1.1.6.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$4 x - 3 x + \frac{- 1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.6.2

Cancel the common factor.

$4 x - 3 x + \frac{- 1}{3} \cdot 3 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.1.6.3

Rewrite the expression.

$4 x - 3 x - 1 = \frac{3}{2} \cdot (9 - x - 6)$

Step 1.2

Subtract $3 x$ from $4 x$ .

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

Step 2

Simplify $\frac{3}{2} \cdot (9 - x - 6)$ .

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Step 2.1

Subtract $6$ from $9$ .

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

Step 2.2

Apply the distributive property.

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

Step 2.3

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

$x - 1 = - \frac{3 x}{2} + \frac{3}{2} \cdot 3$

Step 2.4

Multiply $\frac{3}{2} \cdot 3$ .

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Step 2.4.1

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

$x - 1 = - \frac{3 x}{2} + \frac{3 \cdot 3}{2}$

Step 2.4.2

Multiply $3$ by $3$ .

$x - 1 = - \frac{3 x}{2} + \frac{9}{2}$

Step 3

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

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Step 3.1

Add $\frac{3 x}{2}$ to both sides of the equation.

$x - 1 + \frac{3 x}{2} = \frac{9}{2}$

Step 3.2

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

$x \cdot \frac{2}{2} + \frac{3 x}{2} - 1 = \frac{9}{2}$

Step 3.3

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

$\frac{x \cdot 2}{2} + \frac{3 x}{2} - 1 = \frac{9}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{2} - 1 = \frac{9}{2}$

Step 3.5

Add $x \cdot 2$ and $3 x$ .

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Step 3.5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x + 3 x}{2} - 1 = \frac{9}{2}$

Step 3.5.2

Add $2 \cdot x$ and $3 x$ .

$\frac{5 \cdot x}{2} - 1 = \frac{9}{2}$

$\frac{5 x}{2} - 1 = \frac{9}{2}$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$\frac{5 x}{2} = \frac{9}{2} + 1$

Step 4.2

Write $1$ as a fraction with a common denominator.

$\frac{5 x}{2} = \frac{9}{2} + \frac{2}{2}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{5 x}{2} = \frac{9 + 2}{2}$

Step 4.4

Add $9$ and $2$ .

$\frac{5 x}{2} = \frac{11}{2}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 x = 11$

Step 6

Divide each term in $5 x = 11$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x = 11$ by $5$ .

$\frac{5 x}{5} = \frac{11}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{11}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{5}$

Decimal Form:

$x = 2.2$

Mixed Number Form:

$x = 2 \frac{1}{5}$