Question

||X-3|-3|=3__________​

Answer 1

$| |x - 3| - 3| = 3 \\ |x - 3| - 3 = 3 \\ |x - 3| - 3 = - 3 \\ x = 9 \\ x = - 3 \\ x = 3$

Answer 2

||X-3|-3|=3
Рассмотрим различные случаи:

А. (|х - 3| - 3) = 3:

1) ((х - 3) - 3) = 3
х - 3 - 3 = 3
х = 3 + 6
х1 = 9

2) (-(х - 3) - 3) = 3
-х + 3 - 3 = 3
-х = 3
х2 = -3


Б. -(|х - 3| - 3) = 3

3) -((х - 3) - 3) = 3
-(х - 3 - 3) = 3
-(х - 6) = 3
-х + 6 = 3
-х = 3 - 6
-х = -3
х3 = 3

4) -(-(х - 3) - 3) = 3
-(-х + 3 - 3) = 3
х4 = 3

Ответ: 9; -3; 3








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Answer 3

To solve the equation ||X-3|-3|=3, we'll break it down into cases and solve each one separately. The double absolute value signs indicate that we'll have different solutions depending on the sign of the expression inside the absolute value.

Case 1: (X - 3) - 3 = 3 Simplifying the equation: X - 6 = 3 Adding 6 to both sides: X = 9

Case 2: (X - 3) - 3 = -3 Simplifying the equation: X - 6 = 0 Adding 6 to both sides: X = 6

Case 3: -((X - 3) - 3) = 3 Simplifying the equation: -(X - 6) = 3 Multiplying both sides by -1: X - 6 = -3 Adding 6 to both sides: X = 3

Case 4: -((X - 3) - 3) = -3 Simplifying the equation: -(X - 6) = -3 Multiplying both sides by -1: X - 6 = 3 Adding 6 to both sides: X = 9

Therefore, the solutions to the equation ||X-3|-3|=3 are X = 6 and X = 9.