Solve the equation |3x + 4| = |3x - 11|

Here we have an equation involving absolute values. As a general rule |a| = +a and |a| = -a. We can apply that to our RHS. In the first case we get that 3x + 4 = 3x - 11, however after we subtract 3x from both sides we are left with 4 = -11, which is obviously false. Therefore, we conclude that there are no solutions for |a| = +a and we move on to |a| = -a. Applying our formula again we have 3x + 4 = - (3x - 11) or 3x + 4 = - 3x + 11. Rearranging we get that 6x = 7 or that x = 7/6.