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Functions, 2ADV F1 EQ-Bank 16

Find the values of `x` for which  `|x-3| = 1`.   (2 marks)

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`x=2 or 4`

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`|x-3| = 1`

`text(Method 1)`

`(x-3)^2` `=1`  
`x^2-6x +8` `=0`  
`(x-4)(x-2)` `=0`  

 
`:. x=2 or 4`
 

`text(Method 2)`

`(x-3)` `=1` `-(x-3)` ` = 1`
`x` `=4` `-x +3` `=1`
    `x` `=2`

Functions, 2ADV F1 EQ-Bank 19

Find all values of `x` for which  `| x-4 | = x/2 + 7`.   (3 marks)

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`x = 22\ \ text(or)\ -2`

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`x-4` `= x/2 + 7` `text(or)` `-(x-4)` `= x/2 + 7`
`2x-8` `= x + 14`   `-2x + 8` `= x + 14`
`x` `= 22`   `3x` `= -6`
      `x` `= -2`

 
`:. x = 22\ \ text(or)\ -2`

Functions, 2ADV F1 2019 HSC 13e

  1. Sketch the graph of  `y = |x-1|`  for  `-4 <= x <= 4`.   (1 mark)

  2. Using the sketch from part i, or otherwise, solve  `|x-1| = 2x + 4`.   (2 marks)

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  1. `text(See Worked Solutions)`
  2. `(-1, 2)`
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i.   

 

ii.    `text(By inspection, intersection when)\ x = -1`

`text(Test:)`

`|-1-1|` `= -2 + 4`
`2` `= 2`

 
`:.\ text(Intersection at)\ (-1, 2)`

Functions, 2ADV F1 2008 HSC 1d

Solve  `| 4x-3 | = 7`.   (2 marks)

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`x = 5/2\ \ text(or)\ x = -1`

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`| 4x-3 | = 7`

`4x-3` `= 7` `\ \ \ \ \ -(4x-3)` `= 7`
`4x` `= 10` `-4x + 3` `= 7`
`x` `= 5/2` `-4x` `= 4`
    `x` `= -1`

 

`:. x=5/2\ \ text(or)\ \ -1`

Functions, 2ADV F1 2010 HSC 1d

Solve  `| 2x + 3 | = 9`.   (2 marks)

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 `x = 3\ text(or)\ -6`

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`| 2x + 3 | = 9`

`2x + 3` `=9` `\ \ \ \ -(2x + 3)` `=9`
`2x` `=6` `\ \ \ \ -2x\ – 3` `=9`
`x` `=3` `\ \ \ \ -2x` `=12`
     `x` `=-6`

 

`:. x = 3\ \ text(or)\ \ -6`