As I am self isolating as of now I am having to use a google meet for my maths lessons. As such, the quality is not the best and at some points illegible (Please see below). Actual question is below the first blurry picture!
Actual Question: As a result, since I have no idea how to solve double inequalities as it's my first time, could someone please work through this example question below (step by step please!).
Use set notation to describe the set of values of x for which: $$ x^2 - 7x + 10 <0 \qquad \text{and}\qquad 3x+5<17 $$
Query: I have tried googling this type of question but I keep getting joint inequalities such as $$ -16 \leq 3x+5 \leq 20 $$
Are they the same compared to the question above?
Thank you and any help is much appreciated.
Solving $3x+5<17$ we have $x<4$.
Then $x^2-7x+10=(x-2)(x-5)<0$ is satisfied when $2<x<5$ (draw a sketch!).
But we know that $x<4$. Thus the required solution is $2<x<4$.
See examples here and here.