9.6 Quadratic inequalities — Practise with help

1. $x<4$.
2. $0$, $1$ and $2$.

If an answer differs, revisit Section 9.5 for solving inequalities and Section 9.4 for reading a number line.

Use the inverse operation.

Try the first operation or write the equation before opening the full solution.

$x=-4$.

A product is zero when either factor is zero.

Try the first operation or write the equation before opening the full solution.

$x=1$ or $x=4$.

Substitute 0 into both factors.

Try the first operation or write the equation before opening the full solution.

$(-2)(2)<0$, so the middle interval is not a solution.

Use roots $-2,2$ and test the middle and outer intervals.

Try the first operation or write the equation before opening the full solution.

The expression is positive outside: $x<-2$ or $x>2$.

Factorise and include roots because equality is allowed.

Try the first operation or write the equation before opening the full solution.

$(x-1)(x-3)\leq0$, so $1\leq x\leq3$.