Math Problem Statement

Look at the inequality below.

−6x−4≤−4

Which of these values of x does not make the inequality true? A.−4

Solution

We are given the inequality:

6x44-6x - 4 \leq -4

Step 1: Isolate xx

First, add 4 to both sides to eliminate the constant term on the left-hand side:

6x4+44+4-6x - 4 + 4 \leq -4 + 4

This simplifies to:

6x0-6x \leq 0

Step 2: Solve for xx

Now, divide both sides by 6-6. When dividing by a negative number, remember to reverse the inequality sign:

x0x \geq 0

Step 3: Analyze the options

We need to check which of the given values does not satisfy the inequality x0x \geq 0.

The option provided is x=4x = -4.

Since 4-4 is less than 0, it does not satisfy the inequality x0x \geq 0.

Conclusion:

The value of xx that does not make the inequality true is: 4\boxed{-4}

Would you like further details or have any questions about this solution?

Here are 5 related questions to explore:

  1. How do you solve inequalities involving division by a negative number?
  2. What happens to the inequality sign when multiplying or dividing by a negative number?
  3. How would you represent this inequality on a number line?
  4. What is the difference between strict inequalities and inclusive inequalities?
  5. Can you verify the solution by substituting values into the original inequality?

Tip: Always remember to flip the inequality sign when multiplying or dividing by a negative number!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Inequality manipulation

Theorems

Rule of Inequalities (Multiplying/Dividing by Negative Numbers)

Suitable Grade Level

Grades 6-8