A rectangle has sides of length 4x cm and (x+3)cm and has an area less than 112 cm^2, find the set of values x can take
Derive an inequality for the area. 1) As area = width * length then area is 4x * (x+3). 2) Area is less than ( < ) 112 so inequality is 4x* (x+3) < 112. 3) Expand the brackets and then subtract 112 from both sides to get 4x2 +12x -112 = 0. 4) Divide both sides by 4 to simplify to x2+ 3x -28 = 0. 5) Factorise (x+7)(x-4) = 0 the solutions to x2+3x-28 = y cross the x axis at 4 & -7. 6) As x2+3x-28 < 0 for original inequality to be true and positive shaped graph solutions under the x axis, but as side length can’t be negative or zero actual range of values becomes 0 < x < 4
HT
Related Maths GCSE answers
All answers ▸A t-shirt is in the sale section of a store. It has 20% off and the new sale price is £12. What was the original price of the t-shirt?
How do I factorise a quadratic equation?
In a class of 28 students, the average height of the 12 boys is 1.58 metres. The average height of the class is 1.52 metres. What is the average of the girls?
How do you break down a wordy question (e.g. Aled has three concrete slabs. Two slabs square, of length x, & the third rectangular of dimensions 1m & x+1m. Show 2x^2 +x-6=0 & Solve this)