MYTUTOR SUBJECT ANSWERS

614 views

Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.

For this question, we want to start by finding the possible values of a from the first equation and then using that to give us information about b from the second equation.

Now, the condition that a^2 < 4 actually gives us two pieces of information (a way to remember this is that for inequalities, squared gives us two things). We have that a < 2 but also that a >  -2 since for example, (-3)^2 = 9 which is larger than 4. Therefore, we have -2 < a < 2.

Rearranging the second equation for b, we get b = (8-a)/2. Therefore, putting in our values for a, we get that the maximum value of b is (8-(-2))/2 = 10/2 = 5 and the minimum value of b is (8-2)/2 = 6/2 = 3. Since the inequality for a does not include 2 and -2, we do not include 3 and 5 for b and so we get the answer 3 < b < 5.

Felix S. IB Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor, 13 pl...

1 year ago

Answered by Felix, a GCSE Further Mathematics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

102 SUBJECT SPECIALISTS

£24 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Further Mathematics , Maths+ 3 more

Further Mathematics
Maths
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£24 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics
Maths
Economics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£20 /hr

Abra G.

Degree: Mathematics and Philosophy (Bachelors) - Oxford, St Hugh's College University

Subjects offered:Further Mathematics , Physics+ 6 more

Further Mathematics
Physics
Maths
English
.STEP.
.MAT.
-Personal Statements-
-Oxbridge Preparation-

“Oxford student of Maths and Philosophy looking to share her joy in both. Focusing on first principles, creative problem-solving, and discussion.”

About the author

Felix S.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Further Mathematics , Maths

Further Mathematics
Maths

“About me: Hi, I'm Felix and I'm currently studying for a Mathematics degree at Warwick University. I am very keen to show people not just how to pass maths exams, but how to actuallyenjoy the subject too! I got A* in GCSE Maths and th...”

MyTutor guarantee

|  1 completed tutorial

You may also like...

Posts by Felix

Express 0.545454... as a fraction in its simplest form.

Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.

Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.

Sunita has 75 pens and she ties them into bundles of 8. How many pens does she have left over?

Other GCSE Further Mathematics questions

3x^3 -2x^2-147x+98=(ax-c)(bx+d)(bx-d). Find a, b, c, d if a, b, c, d are positive integers

Solving equations with unknown in both sides

How do you use derivatives to categorise stationary points?

How do I know I can multiply two matrices and if so, how do I do it?

View GCSE Further Mathematics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok