divanshuj wrote:

5< - x

is equal to

x > - 5 right since I am multiplying both sides by - 1

but as per the

OG quant review

5< - x

is equal to

x< - 5

The part highlighted in bold above is incorrect. As 5< -x, multiplying both sides by -1 gives you -5> x (the sign flips), which is the same as saying x< -5, not as you have indicated x > -5. As you have already deduced that -5 is GREATER THAN x, clearly that means x is also LESS THAN -5. So when you switch each value to the opposite side, you will also need to flip the sign around. Eg if 1 is GREATER THAN -2, then -2 is LESS THAN 1.