Solve the following inequalities: x^2+5x+12 > 6Show step by step process to explain the solution and answer

Solve the following inequalities: x^2+5x+12 > 6Show step by step process to explain the solution and answer

Solve the following inequalities: x^2+5x+12 > 6Show step by step process to explain the solution and answer

Solve the following inequalities: x^2+5x+12 > 6Show step by step process to explain the solution and answer
`(x^2+5x+12)gt6`Rearranging,`x^2+5x+6gt0` Changing into factors,`(x+2)(x+3)gt0` For this to be positive, both of the factors are negative or both of the factors are positive.Therefore, one solution is,`x+2lt0 and x+3lt0` `xlt-2` and `xlt-3` The common solution for this is `x lt-3` . The other solution,`x+2gt0` and `x+3gt0` `xgt-2` and `xgt-3` .The common solution is `xgt-2` . Therefore, the solutions for the given inequaility are x <-3 or x>-2.