factoring an inequality

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I was given the inequality x^3 - 8x </= 0 to solve and then graph the solution on a number line.

I have stared at this problem for forever. I've tried to work it out numerous times, but I have no clue how to factor it. I tried taking x from both to make it x(x^2 - 8) but then I'm stuck at a dead end. I have no idea what to do, please help me!

Thanks!
 
To find the zeroes, set this equal to zero.

. . . . .x^3 - 8x = 0

. . . . .x(x^2 - 8) = 0

. . . . .x = 0 or x^2 - 8 = 0

. . . . .x = 0 or x^2 = 8

Now complete the solution by taking roots.

Eliz.
 
still stumped

I don't get this, though b/c you can't take the square root of 8 evenly. I'm not supposed to find the zeros, but solve the inequality and graph it on a number line. Do I still do that then? And if so, I would graph 0 and 2.83 on a number line. But I started out w/ x^3 - 8x greater than or equal to 0. So would I graph the zero and the 2.83 with shaded in dots, the shaded part of the number line being all the numbers below the 2.83 or the 0? I have no clue what I'm doing with this problem.

Thanks.
 
You can't find where the expression is greater than or less than zero until you know where it equals zero (since it will be greater than or less than zero in between these x-values). This is why the first step to solve an inequality is to find the zeroes.

If you have not covered how to solve quadratics by taking roots, then I'm afraid I don't know how the book is expecting you to find the answer to this exercise. Sorry.

Eliz.
 
thanks anyways

ok, thanks for trying! we get ours books friday, which gives us about a week and a half to figure all this out before school starts and this is due so hopefully that will help. thanks!
 
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