Taking Absolute Cases 2 (1 Viewer)

[Lukybear]

This i have a problem with. I was taught to multiply by (x+y)^2 when the x is in the denominator. So for this question of absolutes



The solutions for this, did not require multiplying denomnator by (x+5)^2, but rather took 2 cases. I was wondering what the rules for this is?

 

[Carrotsticks]

I believe that since the denominator is always positive, you can bring it to the other side without worrying about a change of sign.

Once you have brought it to the other side, you can apply the '2 cases' principle associated with absolute values.

 

[Drongoski]

The final inequality you solve as you do in 2U maths.

 

[vafa]

See the attached. (tex source attached as well).

Hope this helps

View attachment 20166

View attachment 20167

 

[cutemouse]

or you could square both sides, since both sides of the inequality are positive.

 

[Lukybear]

Thxs for all kind answers. Especially vafa, for all hard work.

 

[Carrotsticks]

See the attached. (tex source attached as well).

Hope this helps

View attachment 20166

View attachment 20167

what program did you use to do the PDF, graph and the math type?

 

[Lukybear]

What about absolute Qs with variables on both sides?
I.e.

|x-5|<5x+9

 

[gurmies]

|x - 5| < 5x + 9

Solve for |x - 5| = 5x + 9

x - 5 = 5x + 9 or/ x - 5 = -5x - 9

x = -7/2 or/ x = -2/3

After testing x > -2/3, -7/2 < x < -2/3 and x < -7/2; you can deduce that x > -2/3

 

[Trebla]

What about absolute Qs with variables on both sides?
I.e.

|x-5|<5x+9

| x - 5 | < 5x + 9
=> - (5x + 9) < x - 5 < 5x + 9

For this particular question, there is the condition that 5x + 9 ≥ 0 since
5x + 9 > | x - 5 | ≥ 0
hence x ≥ - 9/5 is a restriction

Splitting the inequalities into two parts
x - 5 > - 5x - 9
6x > - 4
x > - 2/3
OR
x - 5 < 5x + 9
4x > - 14
x > - 7/2

To satisfy the three inequalities simultaneously would give x > - 2/3

 

[vafa]

what program did you use to do the PDF, graph and the math type?

TeX for typesetting maths (Getting Started with TeX, LaTeX, and Friends - TeX Users Group)

Pstricks for graphics (/PSTricks/main)