11 Plus Exams Forum

Hi, Happy New Year.

Please can someone help me with these questions, either by directing me to a site that explains it in simple terms or telling me how to work it out in simple steps.

Solve the inequality 10-5x>=5-2x (sorry the the equal to an more than came up as >=)

and
The sum of 3 consecutive whole numbers is less than 33
What are the largest whole numbers that they could be?

I'd appreciate any help please.
X

Inequalities can be solved similar to equations

10-5x>=5-2x
10-5 >= -2x+5x
5 >= 3x
5/3 >= x
x <= 5/3

Now that is the maximum simplification that you can do.
Now x can be any number which is less than (5/3 ~ 1.6666...7)
Generally I have seen questions where it is asked what is the maximum possible whole number for x which in this case would be 1.

The sum of 3 consecutive whole numbers is less than 33
What are the largest whole numbers that they could be?

The sum of 3 consecutives whole number is always a multiple of 3 ( 3 multiplied by the middle number)
The largest multiple of 3 which is less than 33 is 30
Hence the middle number is 10 and hence the set is 9, 10 & 11.

Hope this helps.

Thank you, yes it's all extremely helpful.

With the first question you even answered the part that I forget to ask, which is the smallest integer part.


I've sat down and gone through the rest of his homework with him and he seems to have grasped it now.


Thank you again, when I google it, I just get more and more confused and end up with a headache.

x

I'm glad that is sorted for you rhiane. One thing, if this is a regular issue, I would highly recommend he talk to his teacher (and if he won't then you do). They are best placed to help him learn these skills and if there is something DC is struggling with then the teacher needs to know so that he/she can address them. Good luck.

rhiane wrote: With the first question you even answered the part that I forget to ask, which is the smallest integer part.

Was the question asking for the smallest integer value for x? I answered the largest possible integer.
If the question was asking for smallest, then I think the inequality was incorrect.. unless I am making some blunder. I have double checked twice though

anonymparent wrote:

rhiane wrote: With the first question you even answered the part that I forget to ask, which is the smallest integer part.

Was the question asking for the smallest integer value for x? I answered the largest possible integer.
If the question was asking for smallest, then I think the inequality was incorrect.. unless I am making some blunder. I have double checked twice though

Hi
The question asks "What is the smallest integer that satisfies it?"

He seems to manage most inequality questions ok, but struggles with a few, you are right, he/we need to speak to his teacher which is exactly what I will do this evening via email.
I get so confused with this question type, I'm good at English but worse than useless with this sort of thing.

Many thanks again

Hi again,

Would you say these questions are at the right level for the start of Year 7? they seem quite hard to me!

mad? wrote:I'm glad that is sorted for you rhiane. One thing, if this is a regular issue, I would highly recommend he talk to his teacher (and if he won't then you do). They are best placed to help him learn these skills and if there is something DC is struggling with then the teacher needs to know so that he/she can address them. Good luck.

Thank you.
Yes you are right, I will have a word with the teacher as i'm pretty useless with these questions.
He needs his teacher to explain this to him, he's ok with some inequalities but struggles with some others.

They are effectively treated just the same as if there was just a = sign there for the most part.
However if you multiply or divide both sides by a negative number you need to remember to reverse the inequality. This is the bit they really need to watch for.