Thread: Review questions part 1 - equations involving the absolute value function.

1. Review questions part 1 - equations involving the absolute value function.

Just started university, and I haven't really done math in like a half year at least. Because of this I am struggling a bit on some of the algebra/pre calc review, really would appreciate some help.

Rewrite w/out abs. val. bars
1. |2x - 1| if x < 1/2
2. |2^x + 1|

Solve for x.
3. 1/x+a = 2/x-1 - 1/x-a, where a, b are constants
4. x + (2 times sqrt x) - 3 = 0
5. | (1 - 2x)/x | = 3x
6. x^3 - 5x > or = 4x^2
7. 2/x > or = 3
8. - | 2x + 3 | < -4
9. | 1 - 4x | - 7 < or = 2

Thanks.

I don't think it's allowed to post so much exercices in one time. Start with one exercice, what have you tried? Where are you stuck?

Ok, for example 3.

I realize I have to get the common denominator, but I don't know what to do from there.

Equation 3: (Where's b?)
$\frac{1}{x+a}=\frac{2}{x-1}-\frac{1}{x-a}$
1. You've a rational equation so first make sure the denominator will never be 0 by requiring:
$x\neq a$, $x\neq 1$ and $x\neq -a$
(For example at the end if you come to $x=a$ then you're sure this cannot be the solution!)
2. Put all the terms to one side and make a common denominator:
$\frac{1}{x+a}-\frac{2}{x-1}+\frac{1}{x-a}=0$
$\Leftrightarrow \frac{(x-a)(x-1)}{(x+a)(x-a)(x-1)}-\frac{2(x+a)(x-a)}{(x-1)(x-a)(x+a)}+\frac{(x+a)(x-1)}{(x+a)(x-a)(x-1)}=0$
$\Leftrightarrow \frac{(x-a)(x-1)-2(x+a)(x-a)+(x+a)(x-1)}{(x-a)(x+a)(x-1)}=0$
$\Leftrightarrow (x-a)(x-1)-2(x+a)(x-a)+(x+a)(x-1)=0$

Take it from here.

Originally Posted by xxStrikeback
Just started university, and I haven't really done math in like a half year at least. Because of this I am struggling a bit on some of the algebra/pre calc review, really would appreciate some help.

Rewrite w/out abs. val. bars
1. |2x - 1| if x < 1/2
2. |2^x + 1|

Solve for x.
3. 1/x+a = 2/x-1 - 1/x-a, where a, b are constants
4. x + (2 times sqrt x) - 3 = 0
5. | (1 - 2x)/x | = 3x
6. x^3 - 5x > or = 4x^2
7. 2/x > or = 3
8. - | 2x + 3 | < -4
9. | 1 - 4x | - 7 < or = 2

Thanks.
#2 and #3 have been done for you.

Please post some of the remaining questions according to the forum rules (MHF is not a service for answering questions en mass like this), many are similar so choose a few that represent your general difficulty. You will need to show some effort - what you have done and where you get stuck. It looks like you should also be getting help from your instructor or department tutor.