Solve 5(x+3) < 60

Our technique here will be the same used to solve the problem 5(x+3) = 60, but we must take care at each step to decide whether our inequality changes direction.Firstly, we expand the brackets to give 5x + 15 < 60.We now subtract by 15 on both sides, leaving the inequality fixed since addition and subtraction do not change the direction of the inequality.We then have 5x < 45.To solve for x we will divide by 5. Since 5 is positive, the inequality is unchanged.Our solution is therefore x < 9.We could instead have divided by the 5 throughout initially, and solved x + 3 < 12. This is dependent on how the pupil prefers to do the algebra.We could also attempt to represent the problem graphically, plotting the lines y = 5x + 15 and y = 60, finding their point of intersection, and from there deciding for which values of x our inequality holds. This may be a preferred method for pupils who like to visualise problems more physically.