Help! Algebra problems! Absolute Inequalities?

Question

can you help me solve:
I3.5zI > I7I

THANK YOU!

Answer 1

Remember that absolute value is the distance from 0.

If you ask someone WHERE something is, their answer would give you a DISTANCE and a DIRECTION, like "13 miles thata way". Now if you simply ask someone HOW FAR AWAY something is, then the answer is simpler, like "14 light-years".

The positive and negative signs give our numbers direction: did I earn $10 or spend $10? Do I go north 10 km or south 10 km? etc. But some times we don't need direction. This is absolute value: the distance from 0, doesn't matter if it's positve or negative.

To me this problem is asking, "for what values of z is this true?" so the answer would be all numbers you could plug in for z that would make this a true statement. Let's look at it:

|3.5 z| > |7|

First of all we know the absolute value of 7...it's just 7, so simplify:

|3.5 z| > 7

With absolute value problems there are almost always two cases: the thing in the absolute value signs will either be positive of negative:

-3.5 z > 7 or 3.5 z < 7

To figure out z use the same rules of algebra you already know to get z all by itself.

THE BIG DIFFERENCE WHEN SOLVING INEQUALITIES is this: if somewhere along the line while solving the inequality, you end up multiplying or dividing both sides by a NEGATIVE NUMBER, then you MUST FLIP THE INEQUALITY SIGN SO IT POINTS THE OTHER WAY!!! Your teacher can show you why this is necessary. Just do it in the first problem above when you divide both sides by -3.5:

-3.5 z > 7 divide both sides by -3.5 and flip the sign: z < -2

And the other:

3.5 z > 7 divide both sides by 3.5 : z > 2

So the final answer is a combination of both of these:

z < -2 or z > 2

Any value of z that fits one or the other of these conditions will make this inequality true.

Answer 2

22 or z=2

Answer 3

anytime that i see | | around a number it will be that number unless it is a negative number like | -3 | would be 3 instead. The answer to your problem is 3.5z > 7 which you break down to have z > 7/3.5 which mean z > 2 b/c 3.5 is in 7 2 times.

Answer 4

I think it's:

22 or z=2

[because both sides are inside absolute value symbols]

Answer 5

you will possibly desire to sparkling up for the two useful and a damaging: !) | -2x + 5 | > 7 -2x>2 because of the fact that now you're dividing with a damaging, you will possibly desire to swap the sign: x<-a million 2) | -2x + 5 | <-7 -2x<-12 because of the fact which you're dividing with a damaging, you will possibly desire to swap the sign: x>6 So the respond may be: x<-a million OR x>6 wish I helped(: P.S. everytime you're dividing or multiplying by technique of a damaging, you generally might desire to swap the sign.

Answer 6

your answer should be 3.5z>7