Question

2|–3x – 4| – 16 = 4

Answer 1

Решение:

$2|-3x-4|-16=4\\2|-3x-4|=20\\|-3x-4|=10\\\left \{ {{-3x-4=10} \atop {-3x-4=-10}} \right. \\\left \{ {{-3x=14} \atop {-3x=-6}} \right. \\\left \{ {{x=-\frac{14}{3} =-4\frac{2}{3} } \atop {x=2}} \right.$

Ответ:

$x_1 = -4\frac{2}{3} \\x_2=2$

Answer 2

To solve the equation $2|–3x – 4| – 16 = 4$, you'll need to isolate the absolute value expression and then solve for $x$. Here are the steps to solve it:

1. Start by adding 16 to both sides of the equation to get rid of the -16 on the left side:

   $2|–3x – 4| = 4 + 16$

   $2|–3x – 4| = 20$

2. Now, divide both sides of the equation by 2:

   $|–3x – 4| = \frac{20}{2}$

   $|–3x – 4| = 10$

3. You have an absolute value equation, which means you'll need to consider two cases: one where the expression inside the absolute value is positive and one where it's negative.

   Case 1: $–3x – 4$ is positive:

   $–3x – 4 = 10$

   Now, solve for $x$:

   $-3x = 10 + 4$

   $-3x = 14$

   Divide both sides by -3:

   $x = \frac{14}{-3}$

   $x = -\frac{14}{3}$

   Case 2: $–3x – 4$ is negative:

   $–3x – 4 = -10$

   Now, solve for $x$:

   $-3x = -10 + 4$

   $-3x = -6$

   Divide both sides by -3:

   $x = \frac{-6}{-3}$

   $x = 2$

So, there are two solutions to the equation:

$x = -\frac{14}{3}$ and $x = 2$.