Question

What is the solution set?
It's easy but I'm having the biggest brain fart rn.
|4a + 6| - 4a = -10

Answer 1

you may use the definition of absolute value and see what values of a makes it positive/negative etc but you will be making mistakes

Answer 2

the alternative method is to send that 4a to other side and square both sides

Answer 3

|4a + 6| - 4a = -10


|4a + 6| = 4a-10

(4a+6)^2 = (4a-10)^2

solve a

Answer 4

That method is way too long. My teacher taught
"Drop the bars, set up 2 equations (one the same, other is negated on one side) an then solve"

Answer 5

The first method I mean, is way too long.

Answer 6

got you and i feel the same,
so try the alternative method this time :)

Answer 7

Doesn't work.

Answer 8

@ganeshie8 Once you do it, the \[16a ^{2}\] cancels out

Answer 9

thats right,
does that bother you ?

Answer 10

Yes. So do I just write { } (null set)?

Answer 11

hey no, after expanding you get :

(4a+6)^2 = (4a-10)^2
16a^2+48a+36 = 16a^2-80a+100
48a+36 = -80a+100

solve a

Answer 12

Oh crap, I completely skipped a whole step.
a = .5

When plugged into the original equation, it turns out wrong.

|4a + 6| - 4a = -10
|4(.5) + 6| - 4(.5) = -10
|2 + 6| - 2 = -10
8 - 2 = -10
6 = -10

Answer 13

Looks perfect ! so no solutions

Answer 14

Ah ok! Thank you!

Answer 15

skipping is okay if it is an objective question