We have the equation:

\[
|7m| - 5 = 51
\]

### Step 1: Isolate the absolute value term
Add 5 to both sides of the equation:

\[
|7m| = 56
\]

### Step 2: Solve for \( m \)
Since we are dealing with an absolute value, we consider two cases:
1. \( 7m = 56 \)
2. \( 7m = -56 \)

#### Case 1: \( 7m = 56 \)
Divide both sides by 7:

\[
m = \frac{56}{7} = 8
\]

#### Case 2: \( 7m = -56 \)
Similarly, divide by 7:

\[
m = \frac{-56}{7} = -8
\]

### Final Answer:
The solutions are:

\[
m = 8 \quad \text{or} \quad m = -8
\]

Would you like more details on this or have any other questions?

---

Here are five related questions for further practice:
1. Solve \( |5x| - 3 = 27 \).
2. Solve \( |2n + 4| = 16 \).
3. Solve \( |9p - 7| + 2 = 20 \).
4. What are the solutions to \( |x - 1| + 6 = 14 \)?
5. Solve \( |4y + 9| = 19 \).

**Tip:** When solving absolute value equations, remember to consider both the positive and negative cases.

Learn how to solve the absolute value equation |7m| - 5 = 51 with a detailed, step-by-step solution. This problem introduces concepts in algebra such as solving absolute value equations and isolating variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation