202211041431 Solution to 1977-CE-AMATH-I-2

Find all the values of $x$ which satisfy

$(x+1)^2>16\textrm{ \scriptsize{OR} }2x+5>7$ .

Roughwork.

First,

$\begin{aligned} (x+1)^2 & >16 \\ x^2+2x+1 & >16 \\ x^2+2x-15 & > 0 \\ (x+5)(x-3) & > 0 \\ x<-5 & \textrm{ \scriptsize{OR} }x>3 \\ \end{aligned}$

Second,

$\begin{aligned} 2x+5 & > 7 \\ 2x & > 2 \\ x & > 1 \\ \end{aligned}$

In sum, $x<-5\textrm{ \scriptsize{OR} }x>1$ .

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