Math Problem Statement

Solve the following inequality for m. Write your answer in simplest form: 7m - 8 ≥ 8m - 1

Solution

Let's solve the given inequality:

7m88m17m - 8 \geq 8m - 1

Step 1: Simplify both sides.

Start by subtracting 7m7m from both sides to move the terms with mm to one side:

7m87m8m17m7m - 8 - 7m \geq 8m - 1 - 7m

This simplifies to:

8m1-8 \geq m - 1

Step 2: Solve for mm.

Now, add 1 to both sides to isolate mm:

8+1m-8 + 1 \geq m

Simplifying:

7m-7 \geq m

This is the same as:

m7m \leq -7

Final Answer:

The solution to the inequality is:

m7m \leq -7

Would you like any more details on these steps, or do you have further questions? Here are some related questions to explore:

  1. What happens if you multiply or divide both sides of an inequality by a negative number?
  2. How do you represent the solution m7m \leq -7 on a number line?
  3. Can you explain the difference between \geq and >> in inequalities?
  4. What are the key steps in solving inequalities involving variables on both sides?
  5. How can you check your solution to an inequality?

Tip: When solving inequalities, always remember that reversing the inequality sign is necessary when multiplying or dividing by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Solving Linear Equations

Formulas

-

Theorems

Properties of inequalities
Addition and subtraction of terms

Suitable Grade Level

Grades 7-9