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Question 136386: I have three questions.
1) Solve for x. Collect xs on the leftside, the solution should be present with an x first, the correct inequality symbol, then the number.
3(4x - 5) <9.
2) Solve for x collect xs on the leftside. The solution should be presented with an x first,the corret inequality symbol,then the number.
-7x + 2 + x - 10 >_ -3 (x - 1)
3) Find the midpoint between these points (1,-6) and (-5,-2)
Show all work.
I would like to thank you inadavance for your help.I am confused about algebra.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You solve inequalities in exactly the same fashion you solve equations, with one very important exception. You add equal things to both sides, or you multiply both sides by equal things in order to isolate your variable. You use the distributive, commutative, and associative properties to move terms around conveniently, and you collect like terms. Sometimes you need to find a lowest common denominator in order to combine rational expressions.
The exception is that whenever you multiply both sides of an inequality by a negative number or expression, you must reverse the sense of the inequality (greater than becomes less than or vice versa). Here is a trivial example to illustrate why this rule is necessary:
 is clearly a true statement. However, if you multiply this inequality by -1, you get -2 on the left and -3 on the right. But -2 is greater than, not less than -3, so you have to turn the sign around to maintain the truth of the statement: 
Your third problem can be solved using the mid-point formulas. Given two points, ( , ) and ( , ), the x-coordinate of the midpoint is given by  and the y-coordinate of the midpoint is given by  . Just plug in your coordinate values and do the arithmetic.
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