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Inequalities

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by danjuma » Sun Nov 21, 2010 8:44 pm
Which of the following inequalities has a solution set that when graphed on the numberline, is a single line segment of finite lenght.?

a. X to the fourth power is greater or equal to 1

b. X-cubed is less or equal to 27

c. X-squared is greater or equal to 16

d.. 2 is less or equal to the absolute value of X which is less or equal to 5

e.2 is less or equal to 3x + 4 which is less or equal to 6
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by Night reader » Mon Nov 22, 2010 2:55 am
danjuma wrote:Which of the following inequalities has a solution set that when graphed on the numberline, is a single line segment of finite lenght.?

a. X to the fourth power is greater or equal to 1

b. X-cubed is less or equal to 27

c. X-squared is greater or equal to 16

d.. 2 is less or equal to the absolute value of X which is less or equal to 5

e.2 is less or equal to 3x + 4 which is less or equal to 6
Of the five answer choices eliminate A, B, C as the values of x are not limited on one side, hence not finite; x can extend to the positive (right) or negative (left) sides.

Test D.

2=<|x|=<5
{ 2=<-x and x=<-2
{ 2=<x

{ x=<5
{-x=<5, x=>-5

From this we have two segments: 2=<|x|=<5 and -5=<|x|=<-2. Eliminate D.

Test E if you like

2=<3x+4=<6, -2=<3x=<2 this is finite line. Correct answer E.
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