solve the inequality, help please

khorven said:
2x^2+x<=1
Click to expand...

2x^2 + x - 1 ? 0

(2x - 1)(x + 1) ? 0

Now continue...

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
khorven said:
How do I factor like this?

2x^2 + x - 1
Click to expand...

You could use "trial-and-error" methods.

You could use the "factor by grouping" method.

You could use the Quadratic Formula, to first find the roots.

Personally, I would choose "factor by grouping".

Multiply a*c to get -2

Find two numbers whose product is -2 and whose sum is b

These two numbers are 2 and -1

Use them to rewrite the middle term as a sum of two terms

2x^2 + 2x - x - 1

Group the first two terms, and group the last two terms

(2x^2 + 2x) + (-x - 1)

Factor the first group

2x(x + 1) + (-x - 1)

Factor the second group

2x(x + 1) - (x + 1)

The factor of (x + 1) is common to each side of the difference, factor it out

(x + 1)(2x - 1)

 
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