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...

12 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

Tarryn R.

Degree: Mathematics (Bachelors) - Exeter University

Subjects offered:Further Mathematics , Maths+ 2 more

Further Mathematics
Extended Project Qualification
English Literature

“Hi I'm Tarryn, I'm a Maths student with a wide knowledge in Maths and English Literature modules - I pride myself on being flexible, reliable and enthusiastic!”

£22 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£24 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Further Mathematics , Maths

Further Mathematics

“I'm a fourth year student at Bristol University studying a Masters Degree in Mathematics. ”

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

How many different ways are there to seat 6 people at a round table?

Finding the derivative of a polynomial.

To differentiate a simple equation: y= 4x^3 + 7x

Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.

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