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...

10 months ago

Answered by Felix, a GCSE Further Mathematics tutor with MyTutor

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


£18 /hr

Laura K.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered:Further Mathematics , Science+ 3 more

Further Mathematics

“Hey there! I am Laura and I am currently studying Chemical Engineering at University of Bath. I am really passionate about Science and I am willing to share my knowledge through tutoring you. My passion and expertise in science can be...”

£20 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

£20 /hr

Noah C.

Degree: PPE (Bachelors) - Oxford, Magdalen College University

Subjects offered:Further Mathematics , Politics+ 4 more

Further Mathematics
.TSA. Oxford.

“Hi, I'm Noah. I'm currrently studying Politics, Philosophy and Economics (PPE) at Oxford university. I have always enjoyed teaching others and helping them learn, and my first experience with tutoring was several years of teaching str...”

About the author

Felix S.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Further Mathematics , Maths

Further Mathematics

“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...”

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

What is the range of solutions for the inequality 2(3x+1) > 3-4x?

Solving equations with unknown in both sides

How do I find the limit as x-->infinity of (4x^2+5)/(x^2-6)?

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