Question

1) |–4b – 8| + |–1 – b²| + 2b³ ; b = –2
2) Solve the equation. Check for extraneous solutions.9|9 – 8x| = 2x + 3
please help me and explain step by step. I don't know how to do this

Answer 1

@ljetibo
@dopeness_
@Will.H

Answer 2

split them up in cases. One case where you drop the absolute brackets as if they're positive and one case where you do it as they're negative. From that point on it seems to be a standard cubic equation which you can solve by using the general case formula for finding roots of cubic equations or by trying to extract b and solving for quadratic and a straightforward b=0 equatins.

Answer 3

Im sorry that kinda confuses me even more. @ljetibo

Answer 4

The first problem isn't an equation, but asking you to evaluate the expression for the given value of \(b\); that is, if \(f(b)=|–4b – 8| + |–1 – b^2| + 2b^3\), then what is the value of \(f(-2)\)?

This is just a matter of replacing every instance of \(b\) with \(-2\):
\[|-4(-2)-8|+|-1-(-2)^2|+2(-2)^3=\cdots\]or, simplifying \(f(b)\) a little bit, you can rewrite the first two absolute value terms to get rid of the minus signs:
\[|-4b-8|=\left|(-4)(b+2)\right|=4|b+2|\]and\[|-1-b^2|=|(-1)(b^2+1)|=|b^2+1|=b^2+1\]where the last equality holds because \(b^2+1>0\) for all real \(b\). This just means
\[\begin{align*}
f(-2)&=|-4(-2)-8|+|-1-(-2)^2|+2(-2)^3\\[1ex]
&=4|(-2)+2|+(-2)^2+1+2(-2)^3\\[1ex]
&=\cdots
\end{align*}\]

Answer 5

You can see the step-by-step solution at Calorful: http://goo.gl/c0OnBG
You can use this free calculator to solve algebra questions. You can use it to save time from asking.