Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

A real number X satisfies X cubed is less than 64 is less than X squared. Which statement is correct?  So the first inequality, X cubed is less than 64, tells us that X has to be less than 4. Because 4 cubed is 64 and anything bigger is bigger than 64.  Anything smaller has to be smaller than 64. Well now let's look at this second piece of the inequality.  If X squared is bigger than 64 then we know X is, in absolute value, greater than 8. That means X has to be either less than negative 8 or greater than 8.  Well now let's see which one of these can happen. It can't be these two at the same time, but it can be these two at the same time and that  happens exactly when X is less than negative 8.

Video Summary

A real number X satisfies X cubed is less than 64 is less than X squared. Which statement is correct? So the first inequality, X cubed is less than 64, tells us that X has to be less than 4. Because 4 cubed is 64 and anything bigger is bigger than 64. Anything smaller has to be smaller than 64. Well now let's look at this second piece of the inequality. If X squared is bigger than 64 then we know X is, in absolute value, greater than 8. That means X has to be either less than negative 8 or greater than 8. Well now let's see which one of these can happen. It can't be these two at the same time, but it can be these two at the same time and that happens exactly when X is less than negative 8.

Keywords

real number

inequality

X cubed

X squared

less than negative 8