Null points

Calculate the roots of the equation:

3x+4+3x+5+2x+4=303 |x +4| +3 |x +5| +2 |x +4| = 30


Result

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

Solution:

 x(;5>3(x+4)3(x+5)2(x+4)=30x=8.125(;5> x(5;4>3(x+4)+3(x+5)2(x+4)=30x=17.5(5;4> x(4;+)3(x+4)+3(x+5)+2(x+4)=30x=0.625(4;+) P={8.125,0.625} \ \\ 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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