Basic Math Examples

$- 4 (w + 1) = 2 (1 - 2 w) - 6$

Step 1

Simplify $- 4 (w + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 - 4 (w + 1) = 2 (1 - 2 w) - 6$

Step 1.2

Simplify by adding zeros.

$- 4 (w + 1) = 2 (1 - 2 w) - 6$

Step 1.3

Apply the distributive property.

$- 4 w - 4 \cdot 1 = 2 (1 - 2 w) - 6$

Step 1.4

Multiply $- 4$ by $1$ .

$- 4 w - 4 = 2 (1 - 2 w) - 6$

Step 2

Simplify $2 (1 - 2 w) - 6$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 4 w - 4 = 2 \cdot 1 + 2 (- 2 w) - 6$

Step 2.1.2

Multiply $2$ by $1$ .

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

Step 2.1.3

Multiply $- 2$ by $2$ .

$- 4 w - 4 = 2 - 4 w - 6$

Step 2.2

Subtract $6$ from $2$ .

$- 4 w - 4 = - 4 w - 4$

Step 3

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

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Step 3.1

Add $4 w$ to both sides of the equation.

$- 4 w - 4 + 4 w = - 4$

Step 3.2

Combine the opposite terms in $- 4 w - 4 + 4 w$ .

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Step 3.2.1

Add $- 4 w$ and $4 w$ .

$0 - 4 = - 4$

Step 3.2.2

Subtract $4$ from $0$ .

$- 4 = - 4$

Step 4

Since $- 4 = - 4$ , 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:

$(- \infty, \infty)$