Posted by lauren on Thursday, April 17, 2008 at 8:45pm in response to ALGEBRA.
the problem is 92 is greater than or equal to negative 4p.
why is the answer p is greater than or equal to negative 23?
I am confused! why is it not p is less than or equal to negative 23?
92 >/= -4 p
divide both sides by -4
Rule:
When you multiply or divide both sides of an inequality by a NEGATIVE quantity, you CHANGE the DIRECTION of the arrow
So:
-23 </= p
thank you so much!!! i need that help to finish my homework!!!!
Damon,
Thanks for the help. Let me see if I get it now. So,
-2x < -4
divide both sides by -2
answer is x > 2
I had x < 2, but I reverse the sign since I divided by a -2 on both sides, correct?
To understand why the answer is "p is greater than or equal to -23" instead of "p is less than or equal to -23," we need to solve the inequality and analyze the steps involved.
Here's how to solve the inequality:
1. Start with the given inequality: 92 >= -4p.
2. Divide both sides of the equation by -4. Remember that when dividing by a negative number, the inequality sign flips.
-92/-4 <= -4p/-4 (dividing by -4 on both sides)
23 <= p.
3. We've determined that 23 is less than or equal to p, which means p is greater than or equal to 23.
It seems like there's an error in your question. The correct answer should be "p is greater than or equal to -23" instead of -23 itself, as stated. The solution set for the inequality is p ≥ -23, meaning p can be any value greater than or equal to -23.
To double-check, you can plug in a value for p, such as -20.
Substituting p = -20 into the inequality we get:
92 ≥ -4(-20)
92 ≥ 80
Since 92 is indeed greater than or equal to 80, it confirms that -20 (which is greater than -23) works for the inequality.
In conclusion, p is greater than or equal to -23 because substituting any value greater than or equal to -23 into the inequality will make it true, while substituting any value less than -23 will make it false.