Question

determinati toate numerele intregi x care verifica relatia:
a. |2x - 6|=0
b. |3x - 12|=0
c. |4x + 20|= -6
d. |3x - 27|=0

Answer 1

Răspuns:

a. |2x - 6|=0

|2x - 6|=$\left \{ {{2x-6; 2x-6\geq 0/:2; x\geq3} \atop {6-2x; 2x-6<0/:1; x<3}} \right.$

x≥3⇒ 2x-6=0/:2   x=3  

x<3 ⇒ 6-2x=0/:2  x=3

b. |3x - 12|=0

|3x - 12|= $\left \{ {{3x-12; 3x-12\geq0 /:3; x\geq4} \atop {12-3x; 3x-12<0; x<4}} \right.$

x≥3⇒ 3x-12=0/:3  x=4

x<4⇒ 12-3x=0/:3 x=4

c. |4x + 20|= -6

|4x + 20|=$\left \{ {{4x+20; 4x+20\geq0 /:4; x\geq-5} \atop {-4x-20; 4x+20<0/:4; x<5}} \right.$

x≥-5⇒ 4x+20=-6    4x=-26 /:2    $x=-\frac{13}{2}=-6\frac{1}{2}$ < -5 nu convine

x<-5 ⇒ -4x-20=-6  -4x=14 /:2 $x=-\frac{7}{2}=-3\frac{1}{2}$ > -5 nu convine

d. |3x - 27|=0

|3x - 27|=$\left \{ {{3x-27; 3x-27\geq0 /:3; x\geq 9} \atop {27-3x; 3x-27<0/:3; x<9}} \right.$

x≥9 ⇒ 3x-27=0 /:3   x=9

x<9 ⇒ 27-3x=0/:3  x=9

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