can you please explain number 5 and 7 on Absolute Value

Mike,

I do not understand number 6 in the absolute value section of your book. Why can’t |0| + |7| = 7? Zero is even and 7 is odd.

Mike, in your book you wrote |a| = -a ? I thought the absolute value could only be a positive number.

Test 6 calc section number 28

Hi Mike, I find these Qs confusing and I lose valuable time trying to think my way through them (usually get them wrong anyway!) What’s a good stepwise approach? Thanks!

If 6 < |x-3| < 7 and x < 0, what is one possible value of |x| ?

Subject Test Question:

The area bound by the relationship |x|+|y|=2 is

A) 8

B)1

C) 2

D) 4

E) there is no finite area.

How do you find this algebraically?

Subject Test question:

|2x-1| = 4x+5 has how many numbers in its solution set?

A) 0

B) 1

C) 2

D) an infinite number

E) none of above

How do you find the answer algebraically without graphing it?

How to solve q19, pg 154, from your study guide. Thanks.

For a dog that weighs w pounds and x inches long to qualify for a certain competition, the difference between w and 3/2 x can no more than 5. If a dog with length 24 inches qualify for the competition, what is one possible weight, in pounds, of this dog?

My question regarding making absolute value fall in a particular range. In your book you gave two example (pg 149) and my question is what value should I consider as the end? is it the highest value or the (highest value+1) . Because in question#19 pg149 you consideed 181 to be the end, when 181 isn’t included! & what if the inequality symbol is less than or equal to, what should I do in that case?

Hi mike! This question is from the May 2015 SAT.

(will post photo)

In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?

I’m just going to make up a symbol for better visualization. The symbol will look like this: #

For all numbers x and y, let x # y be defined by x # y= |x^2-y^2| + 2. What is the smallest possible value of x # y?

This was a 2/5 on the difficulty scale yet I somehow didn’t understand this and still got it wrong. I tried to do some weird algebra that got me nowhere so I moved on. Funny thing this was the only question I got wrong in the section.

A 0

B 1

C 2

D 3

E 4

You know the drill by now. The prize this week will, once again, be beta access to the Math Guide, which is really coming along nicely, if I do say so myself. I kinda can’t believe it’s going to top 300 pages, but at this rate we’re definitely heading in that direction. Anyway, to get (more…)

Disclaimer: this is really minor stuff as far as how often it appears on the SAT, so if you’re looking for quick tips to really raise your score, I suggest you start elsewhere. This kind of question is pretty rare. I trust you already know the very basics of absolute value: that |5| = 5, (more…)