Pre-Algebra Examples

$3 (- 2 x - 1) = 2 (x + 5)$

Step 1

Simplify $3 (- 2 x - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (- 2 x - 1) = 2 (x + 5)$

Step 1.2

Simplify by adding zeros.

$3 (- 2 x - 1) = 2 (x + 5)$

Step 1.3

Apply the distributive property.

$3 (- 2 x) + 3 \cdot - 1 = 2 (x + 5)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $- 2$ by $3$ .

$- 6 x + 3 \cdot - 1 = 2 (x + 5)$

Step 1.4.2

Multiply $3$ by $- 1$ .

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

Step 2

Simplify $2 (x + 5)$ .

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Step 2.1

Apply the distributive property.

$- 6 x - 3 = 2 x + 2 \cdot 5$

Step 2.2

Multiply $2$ by $5$ .

$- 6 x - 3 = 2 x + 10$

Step 3

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

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$- 6 x - 3 - 2 x = 10$

Step 3.2

Subtract $2 x$ from $- 6 x$ .

$- 8 x - 3 = 10$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$- 8 x = 10 + 3$

Step 4.2

Add $10$ and $3$ .

$- 8 x = 13$

Step 5

Divide each term in $- 8 x = 13$ by $- 8$ and simplify.

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Step 5.1

Divide each term in $- 8 x = 13$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{13}{- 8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{13}{- 8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{13}{- 8}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{13}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{8}$

Decimal Form:

$x = - 1.625$

Mixed Number Form:

$x = - 1 \frac{5}{8}$