https://file.aiquickdraw.com/mathbot/file/1726832888861azzrjmjo.jpg

The equation provided in the image is:

\[
\frac{|6 - 2m|}{-4} - 7 = -19
\]

Let's solve this step by step.

### Step 1: Simplify the equation
First, isolate the absolute value term by adding 7 to both sides:

\[
\frac{|6 - 2m|}{-4} = -19 + 7
\]

\[
\frac{|6 - 2m|}{-4} = -12
\]

### Step 2: Eliminate the fraction
Multiply both sides by \(-4\) to get rid of the denominator:

\[
|6 - 2m| = (-12)(-4)
\]

\[
|6 - 2m| = 48
\]

### Step 3: Solve the absolute value equation
Now, split the absolute value equation into two cases:

1. \(6 - 2m = 48\)
2. \(6 - 2m = -48\)

#### Case 1: \(6 - 2m = 48\)
\[
-2m = 48 - 6
\]
\[
-2m = 42
\]
\[
m = \frac{42}{-2}
\]
\[
m = -21
\]

#### Case 2: \(6 - 2m = -48\)
\[
-2m = -48 - 6
\]
\[
-2m = -54
\]
\[
m = \frac{-54}{-2}
\]
\[
m = 27
\]

### Final Answer:
The solutions are:
\[
m = -21 \quad \text{or} \quad m = 27
\]

Would you like further details on any step or have any questions?

Here are 5 related questions you might find helpful:
1. How do you handle equations involving absolute values in general?
2. What is the effect of multiplying both sides of an equation by a negative number?
3. How would the problem change if the constant on the right side were positive?
4. How do you graph the solutions of absolute value equations?
5. What are the different methods to check the correctness of your solutions?

**Tip:** Always isolate the absolute value term first when solving such equations for a smoother solution path!

Solve the equation |6 - 2m| / -4 - 7 = -19.

Learn how to solve the absolute value equation |6 - 2m| / -4 - 7 = -19 using algebraic manipulation and properties of absolute values. Step-by-step solution includes isolating the absolute value term, solving two cases, and simplifying the equation. Suitable for Grades 8-10.

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