Trigonometry Examples

$4 (2 w - 4) = 6 (w + 1) + 2 (w - 11)$

Step 1

Since $w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$6 (w + 1) + 2 (w - 11) = 4 (2 w - 4)$

Step 2

Simplify $6 (w + 1) + 2 (w - 11)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 w + 6 \cdot 1 + 2 (w - 11) = 4 (2 w - 4)$

Step 2.1.2

Multiply $6$ by $1$ .

$6 w + 6 + 2 (w - 11) = 4 (2 w - 4)$

Step 2.1.3

Apply the distributive property.

$6 w + 6 + 2 w + 2 \cdot - 11 = 4 (2 w - 4)$

Step 2.1.4

Multiply $2$ by $- 11$ .

$6 w + 6 + 2 w - 22 = 4 (2 w - 4)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $6 w$ and $2 w$ .

$8 w + 6 - 22 = 4 (2 w - 4)$

Step 2.2.2

Subtract $22$ from $6$ .

$8 w - 16 = 4 (2 w - 4)$

Step 3

Simplify $4 (2 w - 4)$ .

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Step 3.1

Apply the distributive property.

$8 w - 16 = 4 (2 w) + 4 \cdot - 4$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $2$ by $4$ .

$8 w - 16 = 8 w + 4 \cdot - 4$

Step 3.2.2

Multiply $4$ by $- 4$ .

$8 w - 16 = 8 w - 16$

Step 4

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

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Step 4.1

Subtract $8 w$ from both sides of the equation.

$8 w - 16 - 8 w = - 16$

Step 4.2

Combine the opposite terms in $8 w - 16 - 8 w$ .

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Step 4.2.1

Subtract $8 w$ from $8 w$ .

$0 - 16 = - 16$

Step 4.2.2

Subtract $16$ from $0$ .

$- 16 = - 16$

Step 5

Since $- 16 = - 16$ , the equation will always be true for any value of $w$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$