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Solve for x÷ ||x-1|-2|=|x-3|
Asked by tusharbailwal8 | 30 Apr, 2019, 08:35: AM
answered-by-expert Expert Answer
G i v e n colon open vertical bar open vertical bar x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar x minus 3 close vertical bar T h e r e space a r e space t h r e e space d i f f e r e n t space c a s e s C a s e space 1 colon space W h e n space x greater or equal than 3 comma space w e space h a v e open vertical bar x minus 1 close vertical bar equals x minus 1 space a n d space open vertical bar x minus 3 close vertical bar equals x minus 3 N o w comma space open vertical bar open vertical bar x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar x minus 1 minus 2 close vertical bar equals open vertical bar x minus 3 close vertical bar equals x minus 3 rightwards double arrow x minus 1 minus 2 equals x minus 3 rightwards double arrow negative 3 equals negative 3 space w h i c h space i s space t r u e C a s e space 2 colon space W h e n space 1 less than x less than 3 space rightwards double arrow x greater than 1 space & space x less than 3 space rightwards double arrow x minus 1 greater than 0 space & space x minus 3 less than 0 W e space h a v e vertical line x minus 1 vertical line equals x minus 1 space & space vertical line x minus 3 vertical line equals negative left parenthesis x minus 3 right parenthesis A l s o comma space open vertical bar open vertical bar x minus 1 close vertical bar minus 2 close vertical bar equals open vertical bar x minus 1 minus 2 close vertical bar equals open vertical bar x minus 3 close vertical bar equals negative left parenthesis x minus 3 right parenthesis rightwards double arrow negative left parenthesis x minus 3 right parenthesis equals negative left parenthesis x minus 3 right parenthesis T h i s space i s space a l s o space t r u e C a s e space 3 colon space W h e n space x less or equal than 1 space rightwards double arrow x less or equal than 1 less than 3 comma space w e space h a v e open vertical bar x minus 1 close vertical bar equals negative left parenthesis x minus 1 right parenthesis space a n d space open vertical bar x minus 3 close vertical bar equals negative left parenthesis x minus 3 right parenthesis rightwards double arrow negative left square bracket negative left parenthesis x minus 1 right parenthesis minus 2 right square bracket equals negative left parenthesis x minus 3 right parenthesis rightwards double arrow x minus 1 plus 2 equals negative x plus 3 rightwards double arrow 2 x equals 2 rightwards double arrow x equals 1 T h u s comma space i t space i s space n o t space t r u e space f o r space x less than 1. H e n c e comma space x element of left square bracket 1 comma infinity right parenthesis
Answered by Renu Varma | 30 Apr, 2019, 10:15: AM

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