Question

A level Quadratic inequality help. See attachment

Answer 1

Answer:

$\huge \green{p = - 1 , q = 4 , r = 6}$

Step-by-step explanation:

First Let solve all three inequalities

$\pink{A } \\ 3x + 5 > 2 \\ \implies \: x > - 1 \\ \implies \: A \in \: ( - 1, \infty )$

$\pink{B} \\ \frac{x}{2} + 1 \leqslant 3\\ \\ \implies \: x \leqslant 4 \\ \implies \: B \in(- \infty ,4]$

$\pink{C} \\ 11 < 2x - 1 \\ \implies \: x > 6 \\ \implies \: C \in \: (6, \infty )$

Now take union of B and C , we get

$B \cup C \in( - \infty ,4] \cup(6, \infty )$

Now take intersection of this set with A

[ I am assuming you know how to take intersection of two sets by drawing them on number line and taking common part out ]

We get

$A \cap(B \cup C) \in \: (- 1,4] \cup \: (6, \infty) \\ \\ or \: this \: can \: be \: written \: as \\ \\x = A \cap(B \cup C) \\ : - 1 < x \leqslant 4 \: \: \cup \: \: x > 6$

Compare it to find value of p , q and r

$p = - 1 \: , \: q = 4 \: ,\: r = 6$

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