smc-6218-10-Absolute Value

Functions, 2ADV EQ-Bank 24

Graph \(y=4\) and \(y=|2 x+2|\) on the same number plane. (2 marks)

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Hence, solve \(|2 x+2|=4\). (1 mark)

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b. \(\text{Solutions occur at graph intersections:}\)

\(\Rightarrow x=1 \ \ \text{or} \ \ x=-3.\)

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b. \(\text{Solutions occur at graph intersections:}\)

\(\Rightarrow x=1 \ \ \text{or} \ \ x=-3.\)

Functions, 2ADV F1 EQ-Bank 14

Solve `|x-2| = 3.` (2 marks)

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`x= -1 or 5`

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`\|\ x-2\ \|`	`= 3`
`(x-2)^2`	`= 3^2`
`(x^2-4x + 4)`	`= 9`
`x^2-4x-5`	`= 0`
`(x-5) (x + 1)`	`= 0`

`:. x= -1 or 5`

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 15

Find the values of `x` for which `|x + 1|= 5`. (2 marks)

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`x = 4 or -6`

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`|x + 1|= 5`

`(x+1)^2`	`= 5^2`
` x^2 + 2x + 1`	`= 25`
`x^2 + 2x-24`	`= 0`
`(x + 6)(x-4)`	`= 0`

`:. x = 4 or -6`

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

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

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

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

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

`text(Test:)`

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

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

Functions, 2ADV F1 2017 HSC 11g

Solve `|3x-1| = 2`. (2 marks)

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`x = 1 or -1/3`

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MARKER’S COMMENT: Note that both conditions must be satisfied!

`|3x-1| = 2`

`3x-1`	`= 2`	`or \ -(3x-1)`	`= 2`
`x`	`= 1`	`-3x`	`= 1`
		`x`	`= -1/3`

`:. x = 1 or -1/3`

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 2009 HSC 1c

Solve `|x + 1|= 5`. (2 marks)

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`x = 4\ \ text(or)\ -6`

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`| x + 1 | = 5`

`(x + 1)`	`= 5`	`\ \ \ \ \ -(x + 1)`	`= 5`
`x`	`= 4`	` -x-1`	`= 5`
		`x`	`= -6`

`:.\ x = 4\ \ text(or)\ -6`

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`