Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Can someone explain to me how to solve this algebraically (i.e. without using plug and chug and/or educated guessing)?

Going the normal route would lead to the following:

x-4=4-x -> x=4 (after getting to this point I understand I can guess above and below 4 to see which one works and then arrive at the correct solution, but I don't want to do this as it is not a rigorous method)

or

-(x-4)=4-x -> -x+4=4-x -> 0=0

So how do we go from these equalities to the inequality that correctly characterizes the solution to this problems:

Can someone explain to me how to solve this algebraically (i.e. without using plug and chug and/or educated guessing)?

Going the normal route would lead to the following:

x-4=4-x -> x=4 (after getting to this point I understand I can guess above and below 4 to see which one works and then arrive at the correct solution, but I don't want to do this as it is not a rigorous method)

or

-(x-4)=4-x -> -x+4=4-x -> 0=0

So how do we go from these equalities to the inequality that correctly characterizes the solution to this problems:

x<=4

Thanks for your input.

We have \(|x-4|=4-x\). \(LHS=|x-4|\) to be equal to \(RHS=4-x\) it should expand with minus sign (in this case -(x-4)=4-x), or which is the same, the expression in absolute value must not be positive: \(x-4\leq{0}\) --> \(x\leq{4}\).

Bunuel, thanks for the explanation and the links. Between the two I think I pieced together the complete correct answer (I think the one you provide is correct but not entirely complete). I will outline the complete answer below (as I understand) and highlight what was missing from your explanation in bold so others can see how to arrive at the answer rigorously. If I go wrong anywhere or my understanding is incorrect please be sure to correct me.

abs(x-4)=4-x

Step 1: Set conditions (consequently the step I was skipping when I first did this problem) a) x-4>=0 b) x-4<0 (you state that this should be x-4<=0 and state that this is where the answer comes from, in actuality this condition is strictly < not <=, in order to get the = part we need to solve (a) as I do below in Step 2 and ensure that it satisfies the condition set out above in Step 1a as I do in Step 3a)

Step 2: Solve the original equations a) x-4=4-x solves to x=4 b) -(x-4)=4-x solves to 0=0

Step 3: Check the solutions to the equations in Step 2 against their respective conditions in Step 1 a) plug x=4 into x-4>=0 which yields 0>=0 which is TRUE hence 4 is a solution to the problem, i.e. x=4 b) because the equation in Step 2b completely cancels out we are left the with the condition from Step 1b as the solution, i.e. x-4<0 or x<4

Combining the possible solutions from Step 3 for both (a) (x=4) and (b) (x<4) (since we have verified that both ARE solutions to the original problem by checking them against the conditions set in Step 1) we come up with the answer to the problem, or x<=4.

I hope you see what I mean when I say that your method wasn't entirely complete. I just want to be very rigorous in solving these is all. However, if my approach is incorrect please do let me know as I will have to go back and re-read the rules on solving these things to make sure I have it down.

Bunuel, thanks for the explanation and the links. Between the two I think I pieced together the complete correct answer (I think the one you provide is correct but not entirely complete). I will outline the complete answer below (as I understand) and highlight what was missing from your explanation in bold so others can see how to arrive at the answer rigorously. If I go wrong anywhere or my understanding is incorrect please be sure to correct me.

abs(x-4)=4-x

Step 1: Set conditions (consequently the step I was skipping when I first did this problem) a) x-4>=0 b) x-4<0 (you state that this should be x-4<=0 and state that this is where the answer comes from, in actuality this condition is strictly < not <=, in order to get the = part we need to solve (a) as I do below in Step 2 and ensure that it satisfies the condition set out above in Step 1a as I do in Step 3a)

Step 2: Solve the original equations a) x-4=4-x solves to x=4 b) -(x-4)=4-x solves to 0=0

Step 3: Check the solutions to the equations in Step 2 against their respective conditions in Step 1 a) plug x=4 into x-4>=0 which yields 0>=0 which is TRUE hence 4 is a solution to the problem, i.e. x=4 b) because the equation in Step 2b completely cancels out we are left the with the condition from Step 1b as the solution, i.e. x-4<0 or x<4

Combining the possible solutions from Step 3 for both (a) (x=4) and (b) (x<4) (since we have verified that both ARE solutions to the original problem by checking them against the conditions set in Step 1) we come up with the answer to the problem, or x<=4.

I hope you see what I mean when I say that your method wasn't entirely complete. I just want to be very rigorous in solving these is all. However, if my approach is incorrect please do let me know as I will have to go back and re-read the rules on solving these things to make sure I have it down.

Thanks again!

It seems that you need to brush up fundamentals on absolute value. So, I do advice to follow the links in my previous posts for that.

As for the solution: it's correct. \(|x-4|=4-x\) to hold true LHS must not be positive which means: \(x-4\leq{0}\) --> \(x\leq{4}\). Exactly as I wrote.

Usually when you expand absolute value you should check when the expression in it is <=0 and >0 (you can put = sign for either of case). But x-4>0 can not hold true as in this case RHS=4-x<0 and we would have that LHS=|x-4|<0 which is cannot possibly be correct as absolute value is always non-negative.

Thanks so much, I hadn't realized that it doesn't matter which condition in Step 1 the = sign was attached to, i.e. as you say it can be to either the > or the < (in the links you provided the = sign always went with the > so I just assumed that this was by rule). This makes your solution completely correct! And everything else follows. Again thank you!

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...