SOLUTION: Solve the following inequality and give its interval notation. -13≤5-2x≤25

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Question 1104966: Solve the following inequality and give its interval notation.
-13≤5-2x≤25
Found 4 solutions by Alan3354, ikleyn, TeachMath, richwmiller:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the following inequality and give its interval notation.
-13 <= 5-2x <= 25
--------------------
13 >= -5+2x >= -25 ---- More about that later.
Add 5
18 >= 2x >= -20
Divide by 2
9 >= x >= -10
-10 <= x <= 9
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Solve the following inequality and give its interval notation.
-13≤5-2x≤25
~~~~~~~~~~~~~~~~~~~~~~~~ 

-13 <= 5 - 2x <= 25


Multiply by -1 all terms.
Since you multiply by NEGATIVE number, CHANGE the inequality signs by the opposite.

You will get


-25 <= 2x - 5 <= 13.


Look ONE MORE time on what you get.


Next, add 5 to all parts of this compound inequality. You will get

-20 <= 2x <= 18.


Divide by 2 all the terms. You will get

-10 <= x <= 9.


It is your answer and your solution.


In interval notation it is  [-10,9].


Answer by TeachMath(96)   (Show Source): You can put this solution on YOUR website!

right answer: - 10 ≤ x ≤ 9
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Teachmath and/or maththerapy
It is an absolute REQUIREMENT that you MUST SHOW ALL WORK. Showing work is the best way to demonstrate your competence. Solutions without sufficient work shown are worthless.
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