Algebra Examples

$8 i x = - 5$

Step 1

Divide each term in $8 i x = - 5$ by $8 i$ .

$\frac{8 i x}{8 i} = \frac{- 5}{8 i}$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

$\frac{8 i x}{8 i} = \frac{- 5}{8 i}$

Step 2.1.2

Rewrite the expression.

$\frac{i x}{i} = \frac{- 5}{8 i}$

Step 2.2

Cancel the common factor of $i$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\frac{i x}{i} = \frac{- 5}{8 i}$

Step 2.2.2

Divide $x$ by $1$ .

$x = \frac{- 5}{8 i}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Multiply the numerator and denominator of $\frac{- 5}{8 i}$ by the conjugate of $8 i$ to make the denominator real.

$x = \frac{- 5}{8 i} \cdot \frac{i}{i}$

Step 3.2

Multiply.

Tap for more steps...

Step 3.2.1

Combine.

$x = \frac{- 5 i}{8 i i}$

Step 3.2.2

Simplify the denominator.

Tap for more steps...

Step 3.2.2.1

Add parentheses.

$x = \frac{- 5 i}{8 (i i)}$

Step 3.2.2.2

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

$x = \frac{- 5 i}{8 (i^{1} i)}$

Step 3.2.2.3

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

$x = \frac{- 5 i}{8 (i^{1} i^{1})}$

Step 3.2.2.4

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

$x = \frac{- 5 i}{8 i^{1 + 1}}$

Step 3.2.2.5

Add $1$ and $1$ .

$x = \frac{- 5 i}{8 i^{2}}$

Step 3.2.2.6

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

$x = \frac{- 5 i}{8 \cdot - 1}$

Step 3.3

Multiply $8$ by $- 1$ .

$x = \frac{- 5 i}{- 8}$

Step 3.4

Dividing two negative values results in a positive value.

$x = \frac{5 i}{8}$