Question

Solve the following Absolute Value Equation. (see comments)

Answer 1

\[\left| 6-4x \right|=\left| 2x-1 \right|\]

Answer 2

\(\huge\color{rde}{WELCOME~TO~OPENSTUDY!!!}\)

Answer 3

we also have to graph it and write the interval notation for it. the teacher hasn't shown us how to do this type yet. just \[>,\le,\ge,<,\]

Answer 4

square both the sides to remove modulus functions. @jpes2193

Answer 5

so i got the solution set {7/6, 5/2} but how would I graph it ?

Answer 6

Alrighty, mate.

For simplicity's sake |A| = |B|
So now, when we remove the modulus, we have two cases for each equation on LHS and RHS - as it is, or with a 'negative' sign next to the entire equation.

Hence, we have 2 options:

A = B
-A = B
-A = -B
A = -B

Since, the last two options mean the same as the first 2, respectively, we can eliminate them, and consider only the first two.

then solve.

Answer 7

plot the modulus function graphs.

Answer 8

the graphs are not to scale but the basic pattern of the graphs would be the same.

Answer 9

See, for the above noted values of X, the equation, y = |6-4x|-|2x-1| becomes zero.

Hence, the two straight lines formed by A and B would mirror from these two points.

An example:

Answer 10

@jpes2193 you can graph it like that

Answer 11

Also, you must have realised the curve never travels below the y=0 line, i.e. X-axis, because, difference of 2 mods, |A| - |B| can NOT be negative.

Answer 12

@apoorvk it would be quite confusing for her. i think i have simplified it nicely what do u say?

Answer 13

Yeah, you can follow Ribhu, his explanation is pretty spot on too. Try visualising.

Answer 14

thanks @apoorvk

Answer 15

@jpes2193 this solves ur graph problem.

Answer 16

@jpes2193 you got this question.

Answer 17

Thanks so Much!!!