Trigonometry Examples

$3 a - (a - 1) = 4 a + 15$

Step 1

Simplify $3 a - (a - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 a - a - - 1 = 4 a + 15$

Step 1.1.2

Multiply $- 1$ by $- 1$ .

$3 a - a + 1 = 4 a + 15$

Step 1.2

Subtract $a$ from $3 a$ .

$2 a + 1 = 4 a + 15$

Step 2

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

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Step 2.1

Subtract $4 a$ from both sides of the equation.

$2 a + 1 - 4 a = 15$

Step 2.2

Subtract $4 a$ from $2 a$ .

$- 2 a + 1 = 15$

Step 3

Move all terms not containing $a$ to the right side of the equation.

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Step 3.1

Subtract $1$ from both sides of the equation.

$- 2 a = 15 - 1$

Step 3.2

Subtract $1$ from $15$ .

$- 2 a = 14$

Step 4

Divide each term in $- 2 a = 14$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 a = 14$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{14}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{14}{- 2}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{14}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $14$ by $- 2$ .

$a = - 7$