# How do you solve the equation abs(1.2-0.3x)=1.5?

Apr 3, 2017

The equation has 2 solutions: ${x}_{1} = - 1$ and ${x}_{2} = 9$. See explanation.

#### Explanation:

First we can see that

$| f \left(x\right) | = a \iff f \left(x\right) = - a \vee f \left(x\right) = a$

So here we have:

$1.2 - 0.3 x = - 1.5 \vee 1.2 - 0.3 x = 1.5$

Both equalities can be divided by $- 0.3$

$- 4 + x = 5 \vee - 4 + x = - 5$

Now if we add $4$ to both sides of both equations we get the solution:

$x = 9 \vee x = - 1$