What is the solution set for abs(2x – 6) – 7 = 7?

Aug 10, 2015

With absolutes you usually end up solving two equations.

Explanation:

But first we simplify, as long as we don't interfere with the sign inside the brackets:

Add 7, then divide by 2:
$\to | 2 x - 6 | = 14 \to | x - 3 | = 7$

Now we have two possibilities:
(1)
$x \ge 3 \to x - 3 \ge 0$ the brackets don't have to do their work:
$x - 3 = 7 \to x = 10$
$x < 3 \to x - 3 < 0$ the brackets flip the sign:
$- \left(x - 3\right) = 7 \to - x + 3 = 7 \to x = - 4$
Answer : $\left\{x = - 4 \mathmr{and} x = + 10\right\}$