algebra 2 help?

Question

Solve the inequality for x: 4 < x – 5 ≤ 6
9 < x ≤ 11
9 ≤ x < 11
-1 < x ≤ 1
-1 ≤ x < 1


Solve the inequality for x: 2 ≤ -5x – 13 < 7
3 ≤ x < 4
3 < x ≤ 4
-4 ≤ x < -3
-4 < x ≤ -3


Solve the inequality for x and graph: -8 < -2x – 1 ≤ -5. Your graph contains _______.
"[" on 2, and "]" on (7/2)
"[" on 2, ")" on (7/2)
"(" on 2, ")" on (7/2)
"(" on 2, "]" on (7/2)

Answer 1

Solve the inequality for x: 4 < x – 5 ≤ 6

To simplify things, you can handle the equality separately.
as such
4 < x – 5 and x – 5 ≤ 6
4+5 < x x ≤ 5+6
9 < x x ≤ 11

Draw these 2 inqualities on a number line and take the overlapping region since the solution for the inequality
4 < x – 5 ≤ 6, involves 9 < x and x ≤ 11. Thus the answer is
9 < x ≤ 11.


Similarly, the next qns, solve the inequality for x: 2 ≤ -5x – 13 < 7, can be tackled. Try it for yourself.

As for your third qns, Solve the inequality for x and graph: -8 < -2x – 1 ≤ -5. Your graph contains _______.

-8 < -2x – 1 ≤ -5
-8 < -2x – 1 and -2x – 1 ≤ -5
-8+1 < -2x -2x ≤ -5+1
-7 < -2x -2x ≤ -4
7 > 2x 4 ≤ 2x
3.5 > x 2 ≤ x
Thus the solution is 2 ≤ x < 3.5
Option 2. "[" on 2, ")" on (7/2)
Cause [ means inclusive. Eg. [2, 3] means 2 to 3 inclusive or 2 ≤ x ≤ 3.
While, ( means not inclusive. Eg. [2,3) means 2 ≤ x < 3

Answer 2

I am a math teacher. Thre first question is A. Separate the inequality into 2 pieces: 4 4 < x – 5
+5 +5
9 < x
x-5 ≤ 6
+5 +5
x ≤ 11
Then put them back together, 9 < x ≤ 11.
Check it out, see if it makes sense. If you choose x=10, does it work?
The inequality signs stay the same until you MULTIPLY or DIVIDE by a negative (then they flip the other way).
When you do the second question, notice the -5x. You need to divide each side by -5 to get x alone so make sure you flip the signs.
Notice the -2x on the third question, another negative coeficient, more flipping! ] and [ are for inequality graphs with "or equal to" in them. ) and ( are for the inequalities "less than" or "greater than" only, NOT "or equal to."
Hope this helps.

Answer 3

Simplify/isolate the x-variable: 4 < x - 5 ≤ 6

First: isolate the x-variable by adding 5 with both sides (when you move a term to the opposite side, always use the opposite sign).

4 + 5 < x - 5 + 5 ≤ 6 + 5

4 + 5 < x ≤ 6 + 5

9 < x ≤ 11

P.S. Please complete the rest on your own. The 2nd problem is very similar to the 1st problem.

Answer 4

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http://www.mathsisfun.com/
www.bbc.co.uk/learning/subjects/maths.shtml
http://www.math.com/
www.mathsnet.net
And my math search
http://search.yahoo.com/search?p=maths&fr=yfp-t-429&toggle=1&cop=mss&ei=UTF-8