Question

| x + 3 | + | x - 5 | = 20
Ajutatima sa rezolv prin metoda intervalilor Urgent Va rog

Answer 1

lx+3l=$\left \{ {{x+3;x+3 \geq 0} \atop {-x-3;x+3\ \textless \ 0}} \right. = \left \{ {{x+3;x \geq -3} \atop {-x-3;x\ \textless \ -3}} \right.$
lx-5l=$\left \{ {{x-5;x-5 \geq 0} \atop {5-x;x-5\ \textless \ 0}} \right. = \left \{ {{x-5;x \geq 5} \atop {5-x;x\ \textless \ 5}} \right.$
Daca x∈(-α;-3)⇒-x-3+5-x=20⇔2-2x=20⇔1-x=10⇔-x=9⇔x=-9
Daca x∈[-3;5)⇒x+3+5-x=20⇒in acest caz nu are solutii.
Dacax∈[5;+α)⇒x+3+x-5=20⇔2x-2=20⇔x-1=10⇔x=11
Solutiile sunt :{-9;11}