smc-987-10-Absolute Value

Functions, 2ADV F1 SM-Bank 44

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

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`x= -1 or 5`

Show Worked Solution

`\|\ 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 SM-Bank 42

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

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`x=2 or 4`

Show Worked Solution

`|\ x − 3\ | = 1`

`text(Method 1)`

`(x − 3)^2 = 1`

`x^2 − 6x + 9 = 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 SM-Bank 41

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

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`x = 4 or -6`

Show Worked Solution

`|\ 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 SM-Bank 37

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

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`x = 22\ \ text(or)\ −2`

Show Worked Solution

`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)

--- 6 WORK AREA LINES (style=lined) ---
Using the sketch from part i, or otherwise, solve `|\ x-1\ | = 2x + 4`. (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Show Worked Solution

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)

Show Answers Only

`x = 1 or -1/3`

Show Worked Solution

MARKER’S COMMENT: Note that both conditions must be satisfied! Dealing with negative signs and division for inequalities produced many errors.

`|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)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Show Worked Solution

`|\ 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)

Show Answers Only

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

Show Worked Solution

`|\ 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)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Show Worked Solution

`|\ 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`