Pre-Algebra Examples

$- 2 (x - 6) + 3 x + 2 - 8 = - 5 (x + 3) + 5$

Step 1

Simplify $- 2 (x - 6) + 3 x + 2 - 8$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 2 x - 2 \cdot - 6 + 3 x + 2 - 8 = - 5 (x + 3) + 5$

Step 1.1.2

Multiply $- 2$ by $- 6$ .

$- 2 x + 12 + 3 x + 2 - 8 = - 5 (x + 3) + 5$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $- 2 x$ and $3 x$ .

$x + 12 + 2 - 8 = - 5 (x + 3) + 5$

Step 1.2.2

Simplify by adding and subtracting.

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Step 1.2.2.1

Add $12$ and $2$ .

$x + 14 - 8 = - 5 (x + 3) + 5$

Step 1.2.2.2

Subtract $8$ from $14$ .

$x + 6 = - 5 (x + 3) + 5$

Step 2

Simplify $- 5 (x + 3) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x + 6 = - 5 x - 5 \cdot 3 + 5$

Step 2.1.2

Multiply $- 5$ by $3$ .

$x + 6 = - 5 x - 15 + 5$

Step 2.2

Add $- 15$ and $5$ .

$x + 6 = - 5 x - 10$

Step 3

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

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Step 3.1

Add $5 x$ to both sides of the equation.

$x + 6 + 5 x = - 10$

Step 3.2

Add $x$ and $5 x$ .

$6 x + 6 = - 10$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$6 x = - 10 - 6$

Step 4.2

Subtract $6$ from $- 10$ .

$6 x = - 16$

Step 5

Divide each term in $6 x = - 16$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 x = - 16$ by $6$ .

$\frac{6 x}{6} = \frac{- 16}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 16}{6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 16}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 16$ and $6$ .

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Step 5.3.1.1

Factor $2$ out of $- 16$ .

$x = \frac{2 (- 8)}{6}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 8}{2 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 8}{2 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{- 8}{3}$

Step 5.3.2

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{3}$

Decimal Form:

$x = - 2.\overline{6}$

Mixed Number Form:

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