Math Is Fun Forum

lily-pad

Guest

Inequalities

I have 2 questions that I do not know how to solve it, so can anyone here help me please? 1) 7- 2x ≤ 4x + 10   and 2) 16 - x > 1
thank you .

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: Inequalities

There's four basic things you can do with inequalities without making the inequality false.
1. Add any number to both sides of the equality sign
2. Subtract any number from both sides of the equality sign
3. Multiply or Divide both sides by any positive number
4. Multiply or Divide both sides by any negative number and then change the direction of the equality sign

1)
7 - 2x ≤ 4x + 10 
Adding 2x to both sides (rule 1 above):
7 ≤ 6x + 10
Subtracting 10 from both sides (rule 2 above):
-3 ≤ 6x
Finally, dividing by 6 (rule 3):
-3/6 ≤ x
or: -0.5 ≤ x

2)
16 - x > 1
Subtract 16 from both sides:
- x > -15
Multiply both sides by -1 and change the direction of the equality sign (rule 4):
x < 15

Just remember your four rules (and the special part about changing the direction of the sign in #4) and you'll be just fine.

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.