Question

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

Answer 1

Answer:

(-6, 1)

Step-by-step 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)

Answer 2

Step-by-step explanation:

${:}\longrightarrow$$\sf x^2+5x$

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

${:}\longrightarrow$$\sf x^2+3x+2x+6$

${:}\longrightarrow$$\sf x(x+3)+2 (x+3)$

${:}\longrightarrow$$\sf (x+3)(x+2)$

${:}\longrightarrow$$\sf x+3$

${:}\longrightarrow$$\sf x$