Inequality

replace the equation with 2 equations because IzI is a V shaped curve and I have done 2 for you already

I-2xI<6

EQATION 1
[-2x]<6 for x less than 0 add 2x and -6 to each side
-6<2x
x>-3 for x<0

EQUATION 2
-[-2x]<6 for x>0
2x<6
x<3

-3< x < 3 answer

Arthur
 
TStiles4 said:
How would this be solved?

|-2x| < 6
Click to expand...

As I stated in a previous answer, it helps to understand that "absolute value" means "distance from 0 on the number line."

If the absolute value of something is less than 6, then that "something" must be less than 6 units from 0 on the number line. Anything that is less than 6 units from 0 on the number line must lie between -6 and 6, right?

So, |-2x| < 6 means that

-6 < -2x < 6

Solve that for x...
 
MRSPI I like your approach. I try to get the student to "see" the curve. Your approach is better

-6<-2x<6 solve for x
the student will probably devide by -2 getting
3 < x <-3 a absurdity

I would have mentioned something to the effect of reversing signs if deviding by a negative.

I am not critisizing just mentioning I like your approach over mine, but I would mention changing < goes to >.
Arthur
 
arthur ohlsten said:
MRSPI I like your approach. I try to get the student to "see" the curve. Your approach is better

-6<-2x<6 solve for x
the student will probably devide by -2 getting
3 < x <-3 a absurdity

I would have mentioned something to the effect of reversing signs if deviding by a negative.

I am not critisizing just mentioning I like your approach over mine, but I would mention changing < goes to >.
Arthur
Click to expand...

Thanks, Arthur...I hoped the student (at this point in dealing with inequalities) would recall that multiplying or dividing both sides of an inequality by a negative number would reverse the direction of the inequality symbols.

I HOPE a student can find the answer him/herself, given a pointer or two, without my handing the answer out on a platter.
 
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