Absolute value of x^2 - 16 is greater than or equal to 9
When Greg solved it in the solution video, he immediately got the two solutions for first inequality as x is greater than or equal to 5, and x is less than or equal to -5 and for the second inequality, x is less than or equal √7 or x is greater than or equal to -√7.
In the practice videos, we were advised to test values on both sides of the solution to confirm the correct inequality sign, i.e in this case, we would test 6 and 3, then also test -3 and -6, to see which values satisfy the first inequality, then do the same for the second one - so lots of testing.
What I’m wondering is whether, in questions like this, I can always assume the solution signs are always opposites of each other? e.g if I test the +ve x value and confirm the sign as “greater than/equal to”, then can I automatically assume the -ve value should have the opposite sign “less than/equal to”?
So ultimately, instead of having up to 8 test cases, I would just need 2 tests to confirm all solution signs 