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
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