Question

What is the solution set to the inequality 5(x − 2)(x + 4) > 0?

Answer 1

Answer:

B. {x| x > 2 or x < -4}

Step-by-step explanation:

Given

$5(x - 2)(x + 4) > 0$

Required

Solve

$5(x - 2)(x + 4) > 0$

Start by dividing both sides by 5

$\frac{1}{5} * 5(x - 2)(x + 4) > \frac{0}{5}$

$(x - 2)(x + 4) > 0$

Find critical point of the inequality by changing the inequality to equality

$(x - 2)(x + 4) = 0$

Split the above expression

$x - 2= 0\ or\ x + 4= 0$

Make x the subject of formula in both

$x - 2+2= 0+2\ or\ x + 4-4= 0-4$

$x = 0+2\ or\ x = 0-4$

$x = 2\ or\ x = -4$

Check the intervals in between the critical points

Set: $x < -4$ --- This works in the inequality

Set: $x > -4$ --- This doesn't work in the inequality

Set: $-4$ --- This doesn't works in the inequality

Set: $x > 2$ --- This works in the inequality

Hence, the solution is: {x| x > 2 or x < -4}