# How do you solve 2ix - 5 + 3i = (2 - i)x + i?

Dec 5, 2015

$x = \frac{\left(- 16 - 11 i\right)}{5}$

#### Explanation:

Given: $2 i x - 5 + 3 i = \left(2 - i\right) x + i$

Multiply out the brackets

$2 i x - 5 + 3 i = 2 x - i x + i$

Collecting like terms

$\left(2 i x + i x\right) + \left(3 i - i\right) - 2 x - 5 = 0$

$x \left(3 i\right) + 2 i - 2 x - 5 = 0$

$x \left(- 2 + 3 i\right) + \left(- 5 + 2 i\right) = 0$

$x = \frac{\left(5 - 2 i\right)}{\left(- 2 + 3 i\right)} \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left(1\right)$

Using $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$
Multiply equation (1) by 1 in the form of $\frac{\left(- 2 - 3 i\right)}{\left(- 2 - 3 i\right)}$

$x = \frac{\left(5 - 2 i\right) \left(- 2 - 3 i\right)}{\left(- 2 + 3 i\right) \left(- 2 - 3 i\right)} \textcolor{w h i t e}{. .} = \textcolor{w h i t e}{. .} \frac{- 16 - 11 i}{5}$