A2a – Substituting numerical values into formulae and expressions

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Substituting numerical values into formulae and expressions

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  1. Find a possible value of \(n\) so that \(n+7\) is less than \(2n\).
  2. Find a possible value of \(n\) so that \(n+7\) is more than \(2n\).
  3. Find the value of \(n\) such that \(n+7=2n\).

  1. Find a possible value of \(x\) so that \(x+8\) is less than \(3x\).
  2. Find a possible value of \(x\) so that \(x+8\) is more than \(3x\).
  3. Find the value of \(x\) such that \(x+8=3x\).
  4. Can you find the value of \(x\) such that \(x+7=3x\)?

  1. Find a set of values of \(p\), \(q\), and \(r\) such that \(\dfrac{p+q}{r}=1\), where \(p\), \(q\), and \(r\) are positive integers.
  2. Find a different set of values of \(p\) \(q\), and \(r\) such that \(\dfrac{p+q}{r}=1\), where \(p\), \(q\), and \(r\) are positive integers.
  3. Find a set of values of \(p\), \(q\), and \(r\) such that \(\dfrac{p+q}{r}=1\) and \(p+q+r=25\).
In the real world

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What next?
Substitution is a fundamental skill in algebra, along with solving equations. You will use it in many contexts. Two basic situations in which you will use substitution are (1) to plot a graph given its equation and (2) to use formulas to work out some useful information, such as the area of a shape: