SOLUTION: Solve - 3/4 x>_ -5/8 The solution set is Can someone please help with this one. This time I am actually getting some of my home work done AND understand it. This chapte

Question 138240: Solve
- 3/4 x>_ -5/8
The solution set is
Can someone please help with this one. This time I am actually getting some of my home work done AND understand it. This chapter is easier than the last few have been. or at least so far it (I dont wanna speak too soon) Thanks.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Solve inequalities in the same manner you solve equations, with one important exception. If you need to multiply (or divide) by a negative number, then you must reverse the sense of the inequality. That is, 'greater than' becomes 'less than' and vice versa.

Here's a trivial example to illustrate why:

Clearly , but if we multiply both sides by -1, you get -2 on the left and -3 on the right. But now you have to turn the inequality sign around because -2 is, in fact, greater than -3.

Multiply both sides by -4:

(notice that the inequality sign reversed)

Multiply both sides by 2:
(inequality sign stayed the same because of multiplication by a positive)

Divide by 6:

Check your answer:

That's true.

Pick a number LARGER than 5/6, say 1

. Oops, not true. But we expected that because x has to be less than or equal to 5/6.

Pick a number SMALLER than 5/6, say 0

. Yep, 0 is greater than any negative number. True.

So, we have shown that the original equation is true at the boundry, and smaller than the boundry, but false larger than the boundary, so the less than or equal relationship in the answer holds. Now the only thing you need is to put your answer into set notation because the question asked for the solution set. {x|} (read: 'The set of all x such that )

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