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

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Answer 1 · 2018-03-13T02:20:30

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

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:

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

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

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