Trigonometry Examples

$15 (x - 1) = - 3 (5 - x) + 12 x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Add $3 (5 - x)$ to both sides of the equation.

$15 (x - 1) + 3 (5 - x) = 12 x$

Step 1.2

Subtract $12 x$ from both sides of the equation.

$15 (x - 1) + 3 (5 - x) - 12 x = 0$

Step 2

Simplify $15 (x - 1) + 3 (5 - x) - 12 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$15 x + 15 \cdot - 1 + 3 (5 - x) - 12 x = 0$

Step 2.1.2

Multiply $15$ by $- 1$ .

$15 x - 15 + 3 (5 - x) - 12 x = 0$

Step 2.1.3

Apply the distributive property.

$15 x - 15 + 3 \cdot 5 + 3 (- x) - 12 x = 0$

Step 2.1.4

Multiply $3$ by $5$ .

$15 x - 15 + 15 + 3 (- x) - 12 x = 0$

Step 2.1.5

Multiply $- 1$ by $3$ .

$15 x - 15 + 15 - 3 x - 12 x = 0$

Step 2.2

Combine the opposite terms in $15 x - 15 + 15 - 3 x - 12 x$ .

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Step 2.2.1

Add $- 15$ and $15$ .

$15 x + 0 - 3 x - 12 x = 0$

Step 2.2.2

Add $15 x$ and $0$ .

$15 x - 3 x - 12 x = 0$

Step 2.3

Subtract $3 x$ from $15 x$ .

$12 x - 12 x = 0$

Step 2.4

Subtract $12 x$ from $12 x$ .

$0 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.