Algebra Examples

$- 5 (- 6 x - 6) = 8 + \frac{4}{3} (\frac{3}{2} x - 6) + 5 x$

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.

$8 + \frac{4}{3} \cdot (\frac{3}{2} x - 6) + 5 x = - 5 (- 6 x - 6)$

Step 2

Simplify $8 + \frac{4}{3} \cdot (\frac{3}{2} x - 6) + 5 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$8 + \frac{4}{3} \cdot (\frac{3 x}{2} - 6) + 5 x = - 5 (- 6 x - 6)$

Step 2.1.2

Apply the distributive property.

$8 + \frac{4}{3} \cdot \frac{3 x}{2} + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Factor $2$ out of $4$ .

$8 + \frac{2 (2)}{3} \cdot \frac{3 x}{2} + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.3.2

Cancel the common factor.

$8 + \frac{2 \cdot 2}{3} \cdot \frac{3 x}{2} + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.3.3

Rewrite the expression.

$8 + \frac{2}{3} (3 x) + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Factor $3$ out of $3 x$ .

$8 + \frac{2}{3} (3 (x)) + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.4.2

Cancel the common factor.

$8 + \frac{2}{3} (3 x) + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.4.3

Rewrite the expression.

$8 + 2 x + \frac{4}{3} \cdot - 6 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.5

Cancel the common factor of $3$ .

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Step 2.1.5.1

Factor $3$ out of $- 6$ .

$8 + 2 x + \frac{4}{3} \cdot (3 (- 2)) + 5 x = - 5 (- 6 x - 6)$

Step 2.1.5.2

Cancel the common factor.

$8 + 2 x + \frac{4}{3} \cdot (3 \cdot - 2) + 5 x = - 5 (- 6 x - 6)$

Step 2.1.5.3

Rewrite the expression.

$8 + 2 x + 4 \cdot - 2 + 5 x = - 5 (- 6 x - 6)$

Step 2.1.6

Multiply $4$ by $- 2$ .

$8 + 2 x - 8 + 5 x = - 5 (- 6 x - 6)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $8 + 2 x - 8 + 5 x$ .

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Step 2.2.1.1

Subtract $8$ from $8$ .

$2 x + 0 + 5 x = - 5 (- 6 x - 6)$

Step 2.2.1.2

Add $2 x$ and $0$ .

$2 x + 5 x = - 5 (- 6 x - 6)$

Step 2.2.2

Add $2 x$ and $5 x$ .

$7 x = - 5 (- 6 x - 6)$

Step 3

Simplify $- 5 (- 6 x - 6)$ .

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Step 3.1

Apply the distributive property.

$7 x = - 5 (- 6 x) - 5 \cdot - 6$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $- 6$ by $- 5$ .

$7 x = 30 x - 5 \cdot - 6$

Step 3.2.2

Multiply $- 5$ by $- 6$ .

$7 x = 30 x + 30$

Step 4

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

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Step 4.1

Subtract $30 x$ from both sides of the equation.

$7 x - 30 x = 30$

Step 4.2

Subtract $30 x$ from $7 x$ .

$- 23 x = 30$

Step 5

Divide each term in $- 23 x = 30$ by $- 23$ and simplify.

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Step 5.1

Divide each term in $- 23 x = 30$ by $- 23$ .

$\frac{- 23 x}{- 23} = \frac{30}{- 23}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 23$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 23 x}{- 23} = \frac{30}{- 23}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{- 23}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{30}{23}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{30}{23}$

Decimal Form:

$x = - 1.30434782 \dots$

Mixed Number Form:

$x = - 1 \frac{7}{23}$