How do you solve x(2x+7)0?

2 Answers
Mar 4, 2018

x72orx0

Explanation:

x(2x+7)0

Distribute

(x)(2x)+(x)(7)0

2x2+7x0

Now we need to find the critical points of the inequality!

2x2+7x=0

We need to factorize this again

#x(2x+7)=0

Set factors equal to 0

x=0or2x+7=0

x=0or2x=07

x=0or2x=7

x=0orx=72

Now we need to check the intervals between the critical points!

x72 (This works in original inequality)

72x0 (This doesn't work)

x0 (This works)

Thus,

The answer is:

x72orx0

Mar 4, 2018

Use the Sign Chart Method

):

Explanation:

Factor (make sure it is equal to zero) and Solve; this is already factored and equal to zero:
Pretend the inequality sign is an equal sign:

x=0,72

Plot these on a number line:

enter image source here

The two points create 3 sections. Plug in any point into the inequality from each section and check the sign:

4(24+7)0negative times negative is positive, this works

2(22+7)0negative times positive is negative, does not work

2(22+7)0positive times positive is positive, this works

Write in interval notation:

(,72]U[0,)

(Use brackets as the answer can be equal to)