Question 1209203: Which of the following are solutions to the inequality below? Select all that apply.
-50<6x+6<-8
x=-7
x=-6
x=-8
x=-1
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'll discuss two methods
Method 1
-50 < 6x+6 < -8
-50-6 < 6x+6-6 < -8-6 .... subtract 6 from all sides
-56 < 6x < -14
-56/6 < 6x/6 < -14/6 .... divide all sides by 6
-9.3333 < x < -2.3333
The decimal values are approximate.
The inequality signs do not flip when we divide all sides by a positive number.
If x is an integer, then the solution set is {-9, -8, -7, -6, -5, -4, -3}
Of your answer choices listed, the solutions are x = -7, x = -6, x = -8
x = -1 is not in that solution set so we cross it off the list.
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Method 2
Since we're given a list of choices, let's try them out one at a time in the original inequality.
Let's try x = -7
-50 < 6x+6 < -8
-50 < 6*(-7)+6 < -8
-50 < -42+6 < -8
-50 < -36 < -8
50 > 36 > 8 ........ multiply all sides by -1; the inequality signs flip
8 < 36 < 50
The last inequality is true.
This means the original inequality is true when x = -7
Therefore, x = -7 is a solution.
You should find that x = -6 and x = -8 are solutions as well.
If we tried x = -1, then,
-50 < 6x+6 < -8
-50 < 6(-1)+6 < -8
-50 < -6+6 < -8
-50 < 0 < -8
8 < 0 < 50 .... after multiplying all sides by -1
This is false since 0 is only between a negative number on the left and a positive number on the right.
x = -1 is crossed off the list.
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Answers:
x = -7, x = -6, x = -8
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