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Linear equations with no solution or every solution

Linear equations with no solution or every solution

IP 1
7 marks
  1. The equation \(3(x-k)=2x+5\) has solution \(x=4\). Find the value of \(k\).[2]
  2. Show that the equation \(2(3x-1)=6x+c\) has no solution when \(c\ne-2\).[2]
  3. Describe the solutions of the equation in part (b) when \(c=-2\).[1]
  4. Find the value of the constant \(p\) for which the equation \(p(x+2)=3x+7\) has no solution.[2]

Solution:

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Answer:(a) \(k=-\dfrac13\) (b) the equation reduces to \(-2=c\), false when \(c\ne-2\) (c) every value of \(x\) is a solution (d) \(p=3\)

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