Inequalities Help

[Helpme121Pls]

Hello,

So I was on the BBC bitesize website revising/researching inequalities. I clicked the test section and came across a questions which got me confused.

Question: -2x < 7

Answers:
1)
2)
3)


Immediately I was confused I thought you had to get the x value on its own so I took -2 away from boths sides and got X = 7 obviously this was wrong so I randomly clicked on one of the answers to see the correct one and here is what it said:

"Be careful with the

and

symbols.

is

and then dividing by

you should get

on the right-hand side of the inequality. "

This made me even more confused.

Where did the 12 - 5 come from in the first place? It's like it just randomly shown up

 

[pka]

Question: -2x < 7
Answers: 1} \(\displaystyle xd<-3.5\) 2) \(\displaystyle x>-3.5\) 3) \(\displaystyle x>3.5\)

Suppose \(\displaystyle a<0\) and we are to solve \(\displaystyle ax\ge b\) then the solution is \(\displaystyle x\le\frac{b}{a}\)

Suppose \(\displaystyle a<0\) and we are to solve \(\displaystyle ax\le b\) then the solution is \(\displaystyle x\ge\frac{b}{a}\)

 

[Helpme121Pls]

Suppose \(\displaystyle a<0\) and we are to solve \(\displaystyle ax\ge b\) then the solution is \(\displaystyle x\le\frac{b}{a}\)

Suppose \(\displaystyle a<0\) and we are to solve \(\displaystyle ax\le b\) then the solution is \(\displaystyle x\ge\frac{b}{a}\)

I appreciate the help but this made things even more confusing is there a VERY VERY simple way of explaining -2x < 7 answer.
I am very stupid so if someone could make it as simple as possible for my brain to understand i'd be appreciative.

Where did 12-5 come from in the first place ?
and why 12-5?

 

[pka]

I appreciate the help but this made things even more confusing is there a VERY VERY simple way of explaining -2x < 7 answer.
I am very stupid so if someone could make it as simple as possible for my brain to understand i'd be appreciative
Where did 12-5 come from in the first place ?
and why 12-5?

There is no 12-5 anywhere in this thread. Where are you seeing it. YOU are the only one adding it.
The question asks for a solution of \(\displaystyle -2x<7\). The solution is \(\displaystyle x>-3.5\).
That is we divide by \(\displaystyle -2\), \(\displaystyle \frac{7}{-2}=-3.5\) because we divide by a negative number it changes the direction of the inequality.

 

[Dr.Peterson]

So I was on the BBC bitesize website revising/researching inequalities. I clicked the test section and came across a questions which got me confused.

Question: -2x < 7

Answers:
1) View attachment 12267
2) View attachment 12268
3) View attachment 12269

Immediately I was confused I thought you had to get the x value on its own so I took -2 away from boths sides and got X = 7 obviously this was wrong so I randomly clicked on one of the answers to see the correct one and here is what it said:

"Be careful with the

and

symbols.

is

and then dividing by

you should get

on the right-hand side of the inequality. "

This made me even more confused.

Where did the 12 - 5 come from in the first place? It's like it just randomly shown up

Maybe you need to show us the page itself.

Several things don't make sense here. In your work, you mention taking -2 from both sides; but if you mean to subtract -2, there is no -2 being added, and you wouldn't get 7. If you mean divide by -2, you'll get what they presumably say, x > -3.5.

But, worse, if they said 12-5 is involved in the solution, they are doing nonsense, because there is no 12 in the problem to take anything from.

I'm wondering if the problem was really -2x + 5 < 12, and they first subtracted 5 from both sides, so that the right hand side became 12 - 5 = 7, leaving you with -2x < 7 as the second step.

Is it possible that you didn't show us the whole problem? We'll want to see the entire problem, and the entire solution, word for word, in order to be able to explain anything.

 

[Helpme121Pls]

Maybe you need to show us the page itself.

Several things don't make sense here. In your work, you mention taking -2 from both sides; but if you mean to subtract -2, there is no -2 being added, and you wouldn't get 7. If you mean divide by -2, you'll get what they presumably say, x > -3.5.

But, worse, if they said 12-5 is involved in the solution, they are doing nonsense, because there is no 12 in the problem to take anything from.

I'm wondering if the problem was really -2x + 5 < 12, and they first subtracted 5 from both sides, so that the right hand side became 12 - 5 = 7, leaving you with -2x < 7 as the second step.

Is it possible that you didn't show us the whole problem? We'll want to see the entire problem, and the entire solution, word for word, in order to be able to explain anything.

Hope this helps

 

[Dr.Peterson]

Clearly what you quoted earlier is all there is, and their solution is for a different problem. They are wrong.

You might want to contact them to complain.

On the other hand, I hope you see by now that the answer is x > -3.5.

 

[Otis]

There is no 12-5 anywhere in this thread ...

It appears in the op, pka, where the OP explains what the source site says.

\(\;\)

 

[pka]

It appears in the op, pka, where the OP explains what the source site says.

Otis, if you can read the OP carefully you can see that the question was posted and then a non-sequitur is immediately entered into.
There was no effort to connect the \(\displaystyle 12-5\) to anything in the post.

 

[Otis]

Otis, if you can read ...

... no effort to connect the \(\displaystyle 12-5\) to anything in the post.

I wasn't commenting on that, pka.

You claimed the expression 12-5 does not appear in the thread. I simply noted that it does!

You may now storm out of the building ...