Absolute Value

[money9111]

I was going through one of my strategy guides and got tripped up on something. It seems very easy though. It's a general problem, not from an official guide or anything. It's actually from the MGMAT Number Property guide.

When does |x - 4| = 4-x? I feel dumb posing this question, but the answer is x less than or equal to 4. I got x=4. Can someone tell me why it's less than or equal to?

[papgust]

One best way of doing this is plugging numbers instead of doing algebraically.

As you see, when you insert numbers greater than 4, right hand side becomes negative and left hand side becomes positive. So, numbers greater than 4 does not satisfy this equation.

If you insert positive numbers <= 4 OR negative numbers, the left and right hand side gives the same value. So, the equation holds for values <= 4.

[money9111]

when do you know when to solve algebraically vs. plugging in #'s?

[papgust]

Basically, algebraic approach and plugging in approach are two different methods to solve a problem. Most people get hold of both approaches and keep plugging in as a fallback option. On the test day, if you struggle to solve it algebraically, then you could use the plugging in method. So, there is no definite reason on when to solve algebraically or by plugging in. For the scenario mentioned above, you could use pluggin method.

[sars72]

when do you know when to solve algebraically vs. plugging in #'s?

my first inclination is to solve each problem algebraically. However, if I can't go anywhere with the equation at hand, then I resort to pluggin in values based on the answer choices

For this question, |x - 4| = 4-x, i wo,uld break it down to two equations:

taking x-4 to be positive, --> x-4 = 4-x --> 2x = 8 --> x=4

taking x-4 to be negative, --> -(x-4) = 4-x --> -x+4=4-x -> 4=4, so we get nothing for x

since the second equation doesn't solve for x, we can't find the value algebraically and have to resort to plugging in

[money9111]

i try to solve alg. first and then plug in but i wasn't sure if there was a specific rule for a type of question. with this question i thought maybe I missed a rule with absolute values where you need to switch to an inequality... but the above explanations make total sense...