Math Problem Statement

Look at the inequality below.

−6x−4≤−4

Which of these values of x does not make the inequality true? A.2.5

B.0

C.17

D.−4

Solution

To solve the inequality 6x44-6x - 4 \leq -4, follow these steps:

  1. Simplify the inequality by adding 4 to both sides: 6x4+44+4-6x - 4 + 4 \leq -4 + 4 This simplifies to: 6x0-6x \leq 0

  2. Divide both sides by -6 to solve for xx, and remember to reverse the inequality sign when dividing by a negative number: x0x \geq 0

The solution to the inequality is x0x \geq 0, which means any value of xx that is greater than or equal to 0 will satisfy the inequality.

Now, let's check each of the answer choices:

  • A. x=2.5x = 2.5: Since 2.502.5 \geq 0, this value satisfies the inequality.
  • B. x=0x = 0: Since 000 \geq 0, this value satisfies the inequality.
  • C. x=17x = 17: Since 17017 \geq 0, this value satisfies the inequality.
  • D. x=4x = -4: Since 40-4 \geq 0 is false, this value does not satisfy the inequality.

Thus, the answer is D. 4-4.

Would you like more details or have any questions?


Here are 5 related questions to expand the topic:

  1. What happens when dividing inequalities by a negative number?
  2. How would you solve the inequality 3x+2103x + 2 \leq 10?
  3. Can you graph the inequality x0x \geq 0 on a number line?
  4. What is the difference between solving an equation and an inequality?
  5. How do you handle compound inequalities involving "and" or "or"?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Solving Linear Inequalities

Formulas

Inequality manipulation: -6x - 4 ≤ -4
Division by negative numbers in inequalities

Theorems

Rule for reversing inequality signs when multiplying or dividing by negative numbers

Suitable Grade Level

Grades 6-8