Setup and solve the absolute value equation. Don't forget to check for extraneous solutions!
The absolute value of (three x plus five) equals twelve x plus 8.
AAAaannndd the bot gets it wrong yet again!
even fails its own arithmetic and logic!
|3x + 5| = 12x + 8
either x > -5/3
3x+5 = 12x+8
9x = -3
x = -1/3
OR x x < -5/3
-(3x+5) = 12x+8
15x = -13
x = -13/15
This solution is extraneous
The odd thing is that this same question was posted a while back and I corrected it (the same as your answer),
and now the bot is doing it in exactly the same incorrect way,
with the bot's solution even containing this morsel:
...
-9x = 3
x = -3
Who generates these questions which always have the same "poster" as the source and are of the same type ? Is this part of the NEW Jishka ? (LLC)
I am getting very tired of continually having to correct the answers given
by the robot.
To solve the absolute value equation |3x + 5| = 12x + 8, we can split it into two separate equations because the absolute value of a number can be equal to the positive or negative value of that number.
Equation 1: 3x + 5 = 12x + 8
Equation 2: -(3x + 5) = 12x + 8
Let's solve Equation 1:
3x + 5 = 12x + 8
Subtract 3x from both sides:
5 = 9x + 8
Subtract 8 from both sides:
-3 = 9x
Divide both sides by 9:
-3/9 = x
or
-1/3 = x
Now let's solve Equation 2:
-(3x + 5) = 12x + 8
Distribute the negative sign:
-3x - 5 = 12x + 8
Add 3x to both sides:
-5 = 15x + 8
Subtract 8 from both sides:
-13 = 15x
Divide both sides by 15:
-13/15 = x
So we have two potential solutions: x = -1/3 and x = -13/15.
Next, we need to check if these solutions are valid by substituting them into the original equation and verifying that they satisfy the given condition.
For x = -1/3:
|3(-1/3) + 5| = 12(-1/3) + 8
|(-1) + 5| = -4 + 8
|4| = 4
Since |4| equals 4, the first solution is valid.
For x = -13/15:
|3(-13/15) + 5| = 12(-13/15) + 8
|(-39/15) + 5| = (-156/15) + 8
|(26/15) + (75/15)| = (-156/15) + (120/15)
|(101/15)| = (-36/15)
Here, |101/15| does not equal |-36/15|, so the second solution is extraneous and is not valid.
Therefore, the only solution is x = -1/3.
|3x + 5| = 12x + 8
3x + 5 = 12x + 8
3x - 12x = 8 - 5
-9x = 3
x = -3
Checking for extraneous solutions:
|3(-3) + 5| = 12(-3) + 8
|-9 + 5| = -36 + 8
|-4| = -28
4 = 28
This is not true, so the solution is x = -3.