Which number line represents the solution set for the inequality 1x24?

answer b

Step-by-step explanation:

1. First solve the in equality as if it was an equallity.

-1/2x = 4

that is true for x = -8

By that knowledge alone, you can eleminate two of the four answers. The possible candidates for a good answer are now only answers b an d since the start with -8 on the number line.

2. Now carefully interpret the sign in the inequality. It says for what x values in -1/2x is the outcome BIGGER or equal then 4. From point 1 we established already that it is equal at x = -8 so try for one easy value of x.

With that I mean, substitute that easy value of x in the inequality and that will give you a true or false statement.

3. If the inequality results in a TRUE statement, then that will give you a deffinitive indication about which of the two remaining candidate answers is the right one, and you will have found your answer.

My choice for subsrituting an easy number is x = 0.

Just substitute x= 0 in -1/2x >= 4 and you get

( -1/2 * 0 ) >= 4

0>= 4

Because zero is NOT bigger then 4, the resulting statement is FALSE.

At this moment you know that the point x = 0 is NOT a member of the solution on the number line, which excludes solution d.

Now the only remaining solution is answer b which must be the right answer.

EXTRA

Although you have deduced beyond any certainty, that answer b must be the right answer, you still can check your findings 'to be sure' by substituting a number on the numberline of answer b.

BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?

By double checking yourself, it will sort of "undermine" your confidence in your chosen aproach. Basically you are doing something which is strictly not nessasary any more. So I urge you, to basically step over the urge to check yourself, and stick to your found answer.

However, if can not resit the temptation of checking, to see if you actually found the right answer, you could test for x = -10 and then you see:

( -1/2 * -10 ) >= 4

( 5 ) >= 4

Because five is BIGGER then 4 this is a true statement, which confirms that answer b is indeed the right answer.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

hi how are you doing today, if you need just ask me.

step-by-step explanation: