he original problem) is $-1$, so boundary values are not included.","front":"Strict inequality"},{"id":"fc-5","back":"The overlap of two solution sets, used when a question says both inequalities.","front":"Intersection"}],"order":9},{"id":"card-10","type":"content","order":10,"title":"Solving two inequalities at the same time","blocks":[{"id":"block-1","content":"When a question says both inequalities, solve each one separately first. Then keep only the overlap, which is called the intersection."},{"id":"block-2","content":"Consider the system $$x^2+4x-12<0$$ and $$8+3x\\le 10+x.$$"},{"id":"block-3","content":"Factorising the quadratic gives $(x+6)(x-2)<0$, so $-61$","isCorrect":false}],"question":"What is the final solution to the system $x^2+4x-12<0$ and $8+3x\\le 10+x$?","explanation":"C is correct because you need the intersection of the quadratic solution $-60$, the solution is between {{blank:l}} and {{blank:u}}, not including the endpoints."},{"id":"card-14","type":"multi-question","order":14,"questions":[{"id":"mq-1","options":[{"id":"a","text":"$$23$","isCorrect":false},{"id":"c","text":"$$2\\le x\\le 3$","isCorrect":false}],"question":"Solve $x^2-5x+6<0$.","explanation":"The roots of the quadratic $x^2-5x+6=0$ are $x=2$ and $x=3$. Because the parabola opens upward ($a>0$) and the inequality is less than

3.5 Quadratic Inequalities Lesson

3.5 Quadratic Inequalities Lesson