Thread: inequality sign

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

Solve inequalities exactly the same way as you would equalities, except that if you multiply or divide by a negative number, swap the direction of the sign...

Originally Posted by jamesk486

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 ?

is not less than ...

nice one!