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Inequalities, SMB-009

For the expression `x^2 > 5x`, what is the smallest positive whole number  `x`  can be that makes the expression correct?  (2 marks)

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`6`

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`text(If)\ \ x = 6,`

`6^2` `> 5 xx 6`
`36` `> 30\ \ \ =>\ text{correct}`

 

`text(All positive whole numbers smaller than 6 result in:)`

`x^2 = 5x\ \ \ text{(for}\ x=5 text{)}`

`x^2 < 5x\ \ \ text{(for}\ x=4,3,2, …text{)}`

Inequalities, SMB-007 MC

The weight (`w` kilograms) and age (`a` years) of a turtle are related by the following inequality:

\begin{array} {|l|}
\hline
\rule{0pt}{2.5ex}w < 8a-13\ \  \text{for all values of}\ a\ \text{between 1 and 10}\rule[-1ex]{0pt}{0pt} \\
\hline
\end{array}

Which pair of values satisfy this inequality?

  1. `w = 4 and a = 2`
  2. `w = 12 and a = 3`
  3. `w = 18 and a = 4`
  4. `w = 40 and a = 6`
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`C`

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`text(Test each option by trial and error.)`

`text(Consider)\ \ w = 18,\ a = 4,`

`18 < 8 xx 4-13`

`18 < 19\ \ text{(correct)}`
 

`:. w = 18,\ a = 4\ text(satisfies the equation).`

`=>C`

Functions, 2ADV F1 2007 HSC 1b

Solve  `2x-5> -3`  and graph the solution on a number line.  (2 marks)

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`x > 1`
 

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`2x-5` `> -3`
`2x` `> 2`
`x` `> 1`