Solve the quadratic inequality: x^2 - 5x + 4 < 0

x²-5x+4 <0First we ignore the inequality and try to solve the equation x²-5x+4=0, which we do via factorising (x-4)(x-1)=0. x = 4 or x=1We draw the graph using our solution, going through the points on the x axis.We look at where the graph goes underneath the x axis; this is the region where the graph is <0 because the y values are less than 0.The values of x for which the graph goes underneath the x axis is the solution. This is between x=1 and x=4. We write this as 1<x<4, remembering the strict inequality because the question uses a strict inequality. We mustn't deviate from the form of the inequality set by the Q.Problem solved!