# Null points

Calculate the roots of the equation:

$3 |x +4| +3 |x +5| +2 |x +4| = 30$

Correct result:

number of roots:  2
x1 =  -8.13
x2 =  -0.63

#### Solution:

$\ \\ x \in \left(-\infty; -5\right> \Rightarrow -3 (x +4) -3 (x +5) -2 (x +4) = 30 \Rightarrow x = -8.125 \in \left(-\infty; -5\right> \ \\ x \in \left(-5; -4\right> \Rightarrow -3 (x +4) +3 (x +5) -2 (x +4) = 30 \Rightarrow x = -17.5 \notin \left(-5; -4\right> \ \\ x \in \left(-4; +\infty\right) \Rightarrow 3 (x +4) +3 (x +5) +2 (x +4) = 30 \Rightarrow x = -0.625 \in \left(-4; +\infty\right) \ \\ P = \{ -8.125, -0.625 \}$

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