Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finte length??
x^4>1
x^3>=27
2<=|x|<+5
2<=3x+4<=6
x^4>1
x^3>=27
2<=|x|<+5
2<=3x+4<=6
Maxx
I think this one is B - X^3=27. As you go through the inequalities, think about which values of x will satisfy them and then imagine plotting these x values on a number line.
X^4>1...for this equation, raising a negative number to an even power will make the number positive. For example, (-2)^4 = 16 = 2^4. Therefore, this inequality will hold true whenever x is greater than 1 or less than -1. If you plotted this on a number line, you would have a line starting at -1 and going off to negative infinity and a line starting at 1 and going off to positive infinity. So this yields 2 seperate line segments of infinite length.
X^3>=27...since negative numbers raised to an odd power will be negative, we know this can never be true for negative values of x. In addition, we know that 3^3=27, so x must be >=3. Plotting x>=3 on the number line, we get a line starting at 3 and going to infinity in the positive direction. This is a single line segment of infinite length.
2<=|x|<=5...for this to be true, x must be between 2 and 5 or between -2 and -5. Plotting this on the number line yields two line segments of finite length (one between -5 and -2 and another between 2 and 5)
2<=3x+4<=6...by subtracting 4 from each expression, this becomes -2=3x<=2. Dividing by 3 yields -2/3<=x<=2/3. Plotting this on a number line gives a single line segment of finite length between -2/3 and 2/3.
