Super quick question! Please help!?

Question

The solution to (x – 3)(x + 1) ≤ 0 is:

a) x < -1
b) -1 < x < 3
c) -1 ≤ x ≤ 3
d) x > 3

Answer 1

x = 3 or -1

But, since the equation opens up, x must be greater or equal to -1 and less than or equal to 3

ans: C

Answer 2

first you need to solve for the eqn if it was just an equal sign not a less than or equal

so either x = 3 or x = -1 would make that eqn = 0

now lets look at values less than or greater than each of these values

if x > 3, let's say 4, (4-3)(4+1) = (1)*3 = 3 not less than 0
if x < 3 but > -1 let's say 2 (2-3)(2+1) = (-1)(3) = -3 < 0
if x < -1 let's say -2 (-2-3)(-2+1) = (-5)(-2) = 10 not less than 0

so the values that fit this equation are values of x between -1 and 3 as well as equal to -1 and 3

c is your answer

Answer 3

You need to look at the critical areas of the real line: x > 3 , -1
When x>3 you get positive * positive, a number >0 so that doesn't work.

At x = 3 you get 0 so that works

When -1
At x=-1 you get 0 so that works

When x<-1 you get negative * negative, a number > 0 so that doesn't work.

So the answer is C.

Answer 4

c

Answer 5

c