Solve the inequality x^2 + 6x − 7 ≥ 0

Question

i thought it was no solution because it has a denominator of 0 in the quadratic formula

Answer 1

x² + 6x -7 ≥ 0

 

(x+7)(x-1) ≥ 0

 

(x+7)(x-1) = 0 when x = 1 or x = -7

 

Draw a number line: ___________l_________________________l____________

                                                -7                                            1

 

When x ≤ -7, x+7 ≤ 0 and x-1 ≤ 0.  So, (x+7(x-1) ≥ 0.

 

When -7 ≤ x ≤ 1, x+7 ≥ 0 and x-1 ≤ 0.  So, (x+7(x-1) ≤ 0.

 

When x ≥ 1, x+7 ≥ 0 and x-1 ≥ 0.  So, (x+7)(x-1) ≥ 0.

 

Solution set:  (-∞, -7] ∪ [1,∞).

 

Answer 2

Hi Dominique,

 

I just saw your question.

You sound smart and sound like you know a lot of Math, so I can get right to it...

 

Ignore the quadratic equation. Try FOIL. You should get 2 answers. One of them works.

 

Good luck!