Question

Find all x such that x^2+5x<6. Express your answer in interval notation.

Answer 1

Explanation:

`{:}\longrightarrow`
`\sf x^2+5x <6`

`{:}\longrightarrow`
`\sf x^2+5x+6 <0`

`{:}\longrightarrow`
`\sf x^2+3x+2x+6<0`

`{:}\longrightarrow`
`\sf x(x+3)+2 (x+3)<0`

`{:}\longrightarrow`
`\sf (x+3)(x+2)<0`

`{:}\longrightarrow`
`\sf x+3 <0\:or (x+2)<0`

`{:}\longrightarrow`
`\sf x <-3\:or\:x <-2`

Answer 2

(-6, 1)

Explanation:

x^2+5x<6,

x^2+5x-6<0,

(x^2-x) + (6x-6)<0,

x(x-1) + 6(x-1)<0,

(x-1)(x+6)<0,

-6<x<1

Interval Notation: (-6, 1)