Basic Math Examples

$(2 \cdot - 6) - 3 i = 10 - 3 y i$

Step 1

Rewrite the equation as $10 - 3 y i = 2 \cdot - 6 - 3 i$ .

$10 - 3 y i = 2 \cdot - 6 - 3 i$

Step 2

Multiply $2$ by $- 6$ .

$10 - 3 y i = - 12 - 3 i$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $10$ from both sides of the equation.

$- 3 y i = - 12 - 3 i - 10$

Step 3.2

Subtract $10$ from $- 12$ .

$- 3 y i = - 22 - 3 i$

Step 4

Divide each term in $- 3 y i = - 22 - 3 i$ by $- 3 i$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 3 y i = - 22 - 3 i$ by $- 3 i$ .

$\frac{- 3 y i}{- 3 i} = \frac{- 22}{- 3 i} + \frac{- 3 i}{- 3 i}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 y i}{- 3 i} = \frac{- 22}{- 3 i} + \frac{- 3 i}{- 3 i}$

Step 4.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{- 22}{- 3 i} + \frac{- 3 i}{- 3 i}$

Step 4.2.2

Cancel the common factor of $i$ .

Tap for more steps...

Step 4.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{- 22}{- 3 i} + \frac{- 3 i}{- 3 i}$

Step 4.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 22}{- 3 i} + \frac{- 3 i}{- 3 i}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify each term.

Tap for more steps...

Step 4.3.1.1

Multiply the numerator and denominator of $\frac{- 22}{- 3 i}$ by the conjugate of $- 3 i$ to make the denominator real.

$y = \frac{- 22}{- 3 i} \cdot \frac{i}{i} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2

Multiply.

Tap for more steps...

Step 4.3.1.2.1

Combine.

$y = \frac{- 22 i}{- 3 i i} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2

Simplify the denominator.

Tap for more steps...

Step 4.3.1.2.2.1

Add parentheses.

$y = \frac{- 22 i}{- 3 (i i)} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2.2

Raise $i$ to the power of $1$ .

$y = \frac{- 22 i}{- 3 (i^{1} i)} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2.3

Raise $i$ to the power of $1$ .

$y = \frac{- 22 i}{- 3 (i^{1} i^{1})} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{- 22 i}{- 3 i^{1 + 1}} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2.5

Add $1$ and $1$ .

$y = \frac{- 22 i}{- 3 i^{2}} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.2.2.6

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{- 22 i}{- 3 \cdot - 1} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.3

Multiply $- 3$ by $- 1$ .

$y = \frac{- 22 i}{3} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.4

Move the negative in front of the fraction.

$y = - \frac{22 i}{3} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.5

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.3.1.5.1

Cancel the common factor.

$y = - \frac{22 i}{3} + \frac{- 3 i}{- 3 i}$

Step 4.3.1.5.2

Rewrite the expression.

$y = - \frac{22 i}{3} + \frac{i}{i}$

Step 4.3.1.6

Cancel the common factor of $i$ .

Tap for more steps...

Step 4.3.1.6.1

Cancel the common factor.

$y = - \frac{22 i}{3} + \frac{i}{i}$

Step 4.3.1.6.2

Rewrite the expression.

$y = - \frac{22 i}{3} + 1$

Step 4.3.2

Reorder $- \frac{22 i}{3}$ and $1$ .

$y = 1 - \frac{22 i}{3}$