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

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Answer 1 · 2017-04-03T15:51:46

The equation has 2 solutions: $x_{1} = - 1$ $x_1=-1$ and $x_{2} = 9$ $x_2=9$ . See explanation.

First we can see that

$| f (x) | = a \Leftrightarrow f (x) = - a \lor f (x) = a$ $|f(x)|=a iff f(x)=-a vv f(x)=a$

So here we have:

$1.2 - 0.3 x = - 1.5 \lor 1.2 - 0.3 x = 1.5$ $1.2-0.3x=-1.5 vv 1.2-0.3x=1.5$

Both equalities can be divided by $- 0.3$ $-0.3$

$- 4 + x = 5 \lor - 4 + x = - 5$ $-4+x=5 vv -4+x=-5$

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

$x = 9 \lor x = - 1$ $x=9 vv x=-1$

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