Question

Which of the following is not a way to represent the solution of the inequality 2(x - 1) - 12?

A. 2x - 5
B. 2xs - 5
C. -5 ≤ x
D. A number line with a closed circle on -5 and shading to the right

Answer 1

Option D is not a correct way to represent the solution of the inequality 2(x - 1) - 12. The correct solution is x > 7, not x ≥ -5 as option D incorrectly indicates.

Step-by-step explanation:

The question asks to identify which of the following is not a way to represent the solution of the inequality 2(x - 1) - 12. First, we need to simplify and solve the inequality to understand what the solution should look like.

Let's solve the inequality step-by-step:

1. Distribute the 2 into the parentheses: 2(x - 1) - 12 = 2x - 2 - 12.
2. Combine like terms: 2x - 14.
3. Now we have the inequality in the form 2x - 14 > 0, which simplifies to 2x > 14 after adding 14 to both sides.
4. Finally, divide both sides by 2 to isolate x, resulting in x > 7.

Now that we have 'x > 7', let's evaluate the options given:

• A. 2x - 5: This is not the solution we found.
• B. 2xs - 5: This option contains a typo and does not make sense.
• C. -5 ≤ x: This is not the correct solution since x should be greater than 7.
• D. A number line with a closed circle on -5 and shading to the right: This representation is incorrect because we are looking for x > 7, not x ≥ -5.

Therefore, option D is not a way to represent the solution of the inequality 2(x - 1) - 12 because it suggests that the solution is x ≥ -5 instead of x > 7.