##### Algebra Solve an inequality. Write as an interval

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

Solve the inequality

x^3 + 5x^2 >or equal to 4x + 20

Please note that the sign is supposed to have a line under it making it 'or equal to.'

Oct 22nd, 2015

x^3 + 5x^2 >or equal to 4x + 20

we can first ignore the sign and do it this way;

x^3 + 5x^2 = 4x + 20

x^3 + 5x^2 - 4x - 20 = 0

solve for x by factoring by grouping:

(x^3 + 5x^2) - (4x + 20) = 0

factor out common term

x^2(x+5) - 4(x+5) = 0

Factor out the (x+5)

(x+5)(x^2-4) = 0

the x^2-4 is a difference of two squares and thus can be factored more

(x+5)(x+2)(x-2) = 0

set each term to zero and solve for x

x+5 = 0 OR x+2 = 0 OR x-2 = 0
x = -5 OR x = -2 OR x = 2

as interval notation:
(-inf, -5] U [-2,2]

-2 >= x >= 2

Oct 22nd, 2015

I typed it in exactly and it stated it as incorrect

Oct 22nd, 2015

Sorry for that dear! Let have a check on it.

Oct 22nd, 2015

(X+2)(X-2)(X+5)=0
X=-2 SOLUTION
X=2 "
X=-5 "

2<=X=>-5

Oct 22nd, 2015

are your brackets and paratheneses right?

Oct 22nd, 2015

Sure..x should be greater or equal to both 2 and -5

Oct 22nd, 2015

...
Oct 22nd, 2015
...
Oct 22nd, 2015
Oct 18th, 2017
check_circle