SOLUTION: What value of x is in the solution set -2(3x+2)

SOLUTION: What value of x is in the solution set -2(3x+2) > -8x+6 (a) -5 (b) 6 (c) 5 (d) -6

Question 1209252: What value of x is in the solution set -2(3x+2) > -8x+6
(a) -5
(b) 6
(c) 5
(d) -6
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 6 (choice B)

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Work Shown
-2(3x+2) > -8x+6
-6x-4 > -8x+6
-6x+8x > 6+4
2x > 10
x > 10/2
x > 5
Anything larger than 5 is in the solution set.
Of the choices you listed, only x = 6 works as a solution.

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Another approach

Since we're given a list of choices, we can plug them one at a time into the original inequality.
If we get a true statement at the end, then we have a solution.

Let's try choice (a)
Plug in x = -5
-2(3x+2) > -8x+6
-2(3*(-5)+2) > -8*(-5)+6
-2(-15+2) > 40+6
-2(-13) > 46
26 > 46
The last inequality at the end is false, so the original inequality is false when x = -5. We can rule out choice (a)

Now let's try choice (b)
Plug in x = 6
-2(3x+2) > -8x+6
-2(3*6+2) > -8*6+6
-2(18+2) > -48+6
-2(20) > -42
-40 > -42
We arrive at a true claim.
It might help to make a (vertical) number line to see that -40 is larger than -42.
Or you can multiply both sides by -1 to go from -40 > -42 to 40 < 42.
Don't forget to flip the inequality sign when multiplying both sides by a negative number.
The last inequality is true, so the original inequality is true when x = 6
The answer is choice (b)

You should find that x = 5 and x = -6 will make the inequality false, so we can rule out choices (c) and (d).
I'll let the student handle the scratch work for these cases.

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