Questions: Solve. 10-x+2=4 x=

Transcript text: Solve. \[ \begin{array}{l} 10-|x+2|=4 \\ x=\square \end{array} \] (Use a comma to separate answers.)

Solution

Solution Steps

To solve the equation \(10 - |x+2| = 4\), we first isolate the absolute value expression. Then, we consider the two cases for the absolute value: one where the expression inside is positive and one where it is negative. Solve each case separately to find the possible values of \(x\).

Step 1: Understand the Problem

We are given the equation:

\[ 10 - |x + 2| = 4 \]

We need to solve for \(x\).

Step 2: Isolate the Absolute Value

First, we isolate the absolute value expression by subtracting 10 from both sides:

\[ -|x + 2| = 4 - 10 \]

Simplifying the right side gives:

\[ -|x + 2| = -6 \]

Step 3: Remove the Negative Sign

Multiply both sides by \(-1\) to remove the negative sign:

\[ |x + 2| = 6 \]