Pre-Algebra Examples

$4 (w - 3) - 6 w = - 2 (w + 6)$

Step 1

Simplify $4 (w - 3) - 6 w$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 w + 4 \cdot - 3 - 6 w = - 2 (w + 6)$

Step 1.1.2

Multiply $4$ by $- 3$ .

$4 w - 12 - 6 w = - 2 (w + 6)$

Step 1.2

Subtract $6 w$ from $4 w$ .

$- 2 w - 12 = - 2 (w + 6)$

Step 2

Simplify $- 2 (w + 6)$ .

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Step 2.1

Apply the distributive property.

$- 2 w - 12 = - 2 w - 2 \cdot 6$

Step 2.2

Multiply $- 2$ by $6$ .

$- 2 w - 12 = - 2 w - 12$

Step 3

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

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Step 3.1

Add $2 w$ to both sides of the equation.

$- 2 w - 12 + 2 w = - 12$

Step 3.2

Combine the opposite terms in $- 2 w - 12 + 2 w$ .

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Step 3.2.1

Add $- 2 w$ and $2 w$ .

$0 - 12 = - 12$

Step 3.2.2

Subtract $12$ from $0$ .

$- 12 = - 12$

Step 4

Since $- 12 = - 12$ , the equation will always be true for any value of $w$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$