Question

Solve |3x - 4| = 6
a) {-10/3,10/3}
b) {-2/3,10/3}
c) {-2/3,2/3}

Answer 1

To dea with absolute values you need to apply the definition of absloute value OR get rid of it by squaring both sides of the equality.
Let's try it by using the definition of the absolute value:

`\left | \alpha \right | \left \{ {{ \alpha , \alpha \geq 0} \atop {- \alpha , \alpha \ \textless \ 0}} \right.`

So, having that in mind, we must split the initial equation into two.

`\left | 3x-4 \right | \left \{ {{(3x-4), x \geq 4/3} \atop {-(3x-4),x\ \textless \ 4/3}} \right.`
Then, we end up with two equations:

`3x-4=6 \\ -(3x-4)=6`
Both yield the solutions:

`x=10/3 \\ x= -2/3`

So your answer would be the second option