SOLUTION: the problem is: solve for x and graph on a number line. 5 - 3x > 10x - 8 i came up with X > 1 and when i graphed the problem i started at 1 (i drew the circle NOT shadded

Question 131317: the problem is: solve for x and graph on a number line.
5 - 3x > 10x - 8
i came up with X > 1
and when i graphed the problem i started at 1 (i drew the circle NOT shadded in) and drew the arrow going in the positive direction.
i can't figure out the right solution for this problem.
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
5-3X>10X-8
-3X-10X>-8-5
-13X>-13
X<-13/-13 THE > SIGN CHANGES TO A < SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE (-) VALUE.
X<1 ANSWER.
PROOF:
LET X=.9
5-3*.9>10*.9-8
5-2.7>9-8
2.3>1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Add -5 to both sides:

Add -10x to both sides:

Now divide both sides by -13, but remember that if you multiply or divide both sides of an inequality by a negative number, you have to reverse the sense of the inequality. Look at an example using specific numbers:

is clearly a true statement, but if you multiply both sides by a -1, you get on one side and on the other side, but the 'less than' sign is no longer correct because is actually greater than .

So back to your problem:

Divide by -13 and turn the inequality sign around:

So your number line graph should have the open circle at 1, but the arrow needs to go to the left (in the negative direction).

So, let's prove the answer with a couple of examples. 0 is less than 1, so let's substitute 0 for x into the original inequality:

, which is a true statement. So far, so good.

2 is greater than 1, so plug in a 2:

, is most assuredly a false statement. That's a pretty good indication that you have properly defined the solution set interval for your inequality.