Question

resolver para x.\\
|x| - 14 = -10\\
si existe más de una solución, separarlas con comas.\\
si no existe solución hacer clic en
o tiene solución\.\\
x = \boxed{}

Explanation:

Step1: Isolate the absolute value

We start with the equation \(|x| - 14 = -10\). To isolate the absolute value expression \(|x|\), we add 14 to both sides of the equation.
\[
|x| - 14 + 14 = -10 + 14
\]
Simplifying both sides, we get:
\[
|x| = 4
\]

Step2: Solve for \(x\)

The absolute value equation \(|x| = 4\) means that \(x\) can be either 4 or -4 because the absolute value of a number is its distance from zero on the number line, and both 4 and -4 are 4 units away from zero. However, wait, let's check again. Wait, no, in our case, after step 1, we have \(|x| = 4\)? Wait, no, wait: \(-10 + 14 = 4\), so \(|x| = 4\), so \(x = 4\) or \(x = -4\)? Wait, no, that can't be. Wait, no, let's re - examine the original equation: \(|x| - 14=-10\). So adding 14 to both sides: \(|x|= - 10 + 14=4\). So the solutions are \(x = 4\) and \(x=-4\)? Wait, no, that's correct. Wait, but maybe I made a mistake. Wait, no, absolute value of \(x\) equals 4, so \(x = 4\) or \(x=-4\). But wait, let's check the original equation with \(x = 4\): \(|4|-14=4 - 14=-10\), which is correct. With \(x=-4\): \(|-4|-14 = 4-14=-10\), which is also correct. Wait, but the problem says "Si existe más de una solución, separarlas con comas". So we have two solutions: 4 and -4? Wait, no, wait, no, I think I messed up. Wait, no, the original equation is \(|x| - 14=-10\). So \(|x|=4\), so \(x = 4\) or \(x=-4\). But let's check again. Wait, maybe the user made a typo, but according to the equation given, \(|x|-14 = - 10\), so \(|x|=4\), so solutions are \(x = 4\) and \(x=-4\). But wait, maybe I misread the equation. Wait, the equation is \(|x| - 14=-10\), yes. So:

Wait, no, wait, maybe the equation is \(|x - 14|=-10\)? But the user wrote \(|x| - 14=-10\). Let's confirm. The image shows \(|x| - 14=-10\). So, proceeding with \(|x|=4\), so \(x = 4\) or \(x=-4\). But wait, let's check again. If \(x = 4\): \(|4|-14=4 - 14=-10\), correct. If \(x=-4\): \(|-4|-14 = 4-14=-10\), correct. So the solutions are \(x = 4\) and \(x=-4\). But wait, maybe the user intended \(|x - 14|=-10\), but as per the given equation, it's \(|x| - 14=-10\). So the solutions are \(x = 4\) and \(x=-4\). But wait, no, that's correct.

Wait, but maybe I made a mistake. Wait, no, let's do it step by step:

1. Start with \(|x| - 14=-10\)
2. Add 14 to both sides: \(|x|=-10 + 14\)
3. Calculate \(-10 + 14 = 4\), so \(|x| = 4\)
4. The solutions to \(|x|=4\) are \(x = 4\) and \(x=-4\) because \(|4| = 4\) and \(|-4| = 4\)

Answer:

4, - 4