The set of all values of x such that 3 (3 – 2x) ≤ 15 is:
A. x ≤ 1
B. x ≥ 1
C. x ≤ -1
D. x ≤ -2
E. None of the above
does the sign change? not sure
You need to know why the sign would change....
but
If it was temperature, the temperature dropping from 5 would go to 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6.....
How would we go from to
This would happen if we multiply or divide both sides by the same negative value.
Changing signs is the mathematical operation of multiplying or dividing by
It does not matter if we have an equality...
but
Therefore,
You can reverse the inequality also to bring you to the same answer.
Notice above that we did not do any multiplying or dividing by negative numbers,
hence no reversal was ever needed.
Now, multiply (or divide) both sides by to get the co-efficient of x positive.
However, you can add 2x to both sides to also get the co-efficient of x positive.
Getting the co-efficient of x positive is necessary to find it's boundary.
What goes between ?