Question

How do you solve `|2.3 - 5.7x| = 11.4`?

Answer 1

Find the solutions of x that give you `+-11.4` inside the absolute value bars. For that scenario, x=-1.5965 and x=2.4035

Explanation:

Because we're dealing with an absolute value, x can have two solutions since:

`abs(11.4)=11.4` and `abs(-11.4)=11.4`

Therefore, we need to find the following solutions:

`2.3-5.7x = 11.4`
`2.3-5.7x=-11.4`

The first step for both is to subtract 2.3 from both sides, and the second step is to divide by x's coefficient. This gives you the solution:

`x=(11.4-2.3)/(-5.7) rArr x=-9.1/5.7 = -1.5965`

`x=(-11.4-2.3)/(-5.7) rArr x=13.7/5.7 = 2.4035`