Trigonometry Examples

$- 2 (2 - 5 y) = 5 (2 y - 2) + 6$

Step 1

Simplify $- 2 (2 - 5 y)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (2 - 5 y) = 5 (2 y - 2) + 6$

Step 1.2

Simplify by adding zeros.

$- 2 (2 - 5 y) = 5 (2 y - 2) + 6$

Step 1.3

Apply the distributive property.

$- 2 \cdot 2 - 2 (- 5 y) = 5 (2 y - 2) + 6$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $- 2$ by $2$ .

$- 4 - 2 (- 5 y) = 5 (2 y - 2) + 6$

Step 1.4.2

Multiply $- 5$ by $- 2$ .

$- 4 + 10 y = 5 (2 y - 2) + 6$

Step 2

Simplify $5 (2 y - 2) + 6$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 4 + 10 y = 5 (2 y) + 5 \cdot - 2 + 6$

Step 2.1.2

Multiply $2$ by $5$ .

$- 4 + 10 y = 10 y + 5 \cdot - 2 + 6$

Step 2.1.3

Multiply $5$ by $- 2$ .

$- 4 + 10 y = 10 y - 10 + 6$

Step 2.2

Add $- 10$ and $6$ .

$- 4 + 10 y = 10 y - 4$

Step 3

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

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Step 3.1

Subtract $10 y$ from both sides of the equation.

$- 4 + 10 y - 10 y = - 4$

Step 3.2

Combine the opposite terms in $- 4 + 10 y - 10 y$ .

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Step 3.2.1

Subtract $10 y$ from $10 y$ .

$- 4 + 0 = - 4$

Step 3.2.2

Add $- 4$ and $0$ .

$- 4 = - 4$

Step 4

Since $- 4 = - 4$ , the equation will always be true for any value of $y$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$