Search 72,310 tutors FIND TUTORS
Search for tutors
Ask a question
0 0

Solve. |x-1/5|= 3

Solve. |x-1/5|= 3

Comments

first, for |x| = 3, we have x = (+/-)3; so, therefore, by analogy, |x - 1/5| = 3 means that x - 1/5 = 3, or x - 1/5 = -3; in either case, add 1/5 to each side of the equation; in the first equation, we then get x = 3 + 1/5 = 15/5 + 1/5 = 16/5; and in the second equation, we get x = -3 + 1/5 = -15/5 + 1/5 = -14/5

Comment

Tutors, please sign in to answer this question.

3 Answers

Since this deals with an absolute value, meaning (x-1/5) could equal 3 or -3, you need to set up two equations to solve:

x-1/5=3

x-1/5=-3

and then solve each one to get your two answers.

To solve the first, simply add 1/5 to 3 to balance the equation and get x=3 1/5. For the second, do the same thing but get your other possible value of x as x=-2 4/5. 

|x-1/5|= 3

For absolute equations, you actually have two equations you are solving for:

x - 1/5 = 3

and -(x - 1/5) = 3. There you have a negative outside the parentheses, that means you have to just switch the signs around in the parenthesis (aka multiply by -1). 

So you would end up with -x + 1/5 = 3. 

So your two equations to solve for x are:

x - 1/5 = 3 and -x + 1/5 = 3. 

To solve the left equation, add 1/5 to both sides:

x = 3 + 1/5     But you need to change the fractions to get an answer. 

x = 15/5 + 1/5

x = 16/5 this is your first answer. 

Now solve the second equation: -x + 1/5 = 3.

It's pretty much the same thing: except you subtract 1/5 from both sides. 

-x = 3 - 1/5 

now change the fractions 

-x = 15/5 - 1/5

-x = 14/5

x is negative (or multiplied by -1) so in order to find positive x, you need to divide both sides by -1, or just change the signs. 

So you end up with: 

x = 14/5 

and you are done! :)

Comments

Comment

Because of the absolute value signs, there are two conditions to consider: 

1. x - 1/5 = 3

2. -(x - 1/5) = 3   (which can also be written as x - 1/5 = -3)

Solve each of these for x, and you will have your possible x values. 

Comments

Is the problem |(x-1)/5| = 3 (- means both x and -1 are divided by 5), or is it |x - one fifth| = 3??

Comment