Question

Could x = -5 be a solution to the inequality -6 < 3x + 9 < 21?

Answer 1

x=−5<x<4

Explanation:

Answer 2

So you think that x = -5 is the solution for the inequality? Let's check it out.

(Check)

- Substitute x = -5 in the inequality

`-6<3(-5)+9<21\\-6<-15+9<21\\-6<-6<21`

If it was the symbol ≤ you'd be correct, but it's < so It's a bit wrong.

Now let's solve the inequality. Separate the inequality by parts.

`\left \{ {{-6<3x+9} \atop {3x+9<21}} \right. \\\left \{ {{-6-9<3x} \atop {3x<21-9}} \right. \\\left \{ {{-15<3x} \atop {3x<12}} \right. \\\left \{ {{x>-5} \atop {x<4}} \right.`

Therefore, the inequality is true only when x > -5 or x < 4.

(Check)

- Substitute x = -4 in the inequality.

`-6<3(-4)+9<21\\-6<-12+9<21\\-6<-3<21`

The inequality is true for first case.

- Substitute x = 3 in the inequality

`-6<3(3)+9<21\\-6<9+9<21\\-6<18<21`

The inequality is true for second case.

So the answer for inequality is -5 < x < 4

That means only {-4, -3, -2, ..., 3} can make the inequality true.