Solution assignment 10 Linear equations

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Assignment 10

For which value(s) of  p does the following equation have exactly one solution x:

p(x-1)+2=x-2p-1

Solution

We can write this equation as:

(p-1)x=-p-3

(p-1)x=-(p+3)

This equation has only one solution x if:

p\neq1

This means in this case that the solution is:

x=-\displaystyle\frac{p+3}{p-1}

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