Which values for x make this inequality true?
14x+6≥31
Question 2 options:
x> -100
x≤100
x ≥-100
x≥100
the second one of course
14x+6 ≥ 31
14x ≥ 25
x ≥ 25/14
I suspect a typo
D is correct if you meant 1/4 x + 6 ≥ 31
so learn how to type fractions
To solve the inequality 14x + 6 ≥ 31, we need to isolate the variable x. Here's how you do it:
1. Start by subtracting 6 from both sides of the equation to get rid of the constant term. This gives you:
14x + 6 - 6 ≥ 31 - 6
14x ≥ 25
2. Next, divide both sides of the equation by 14 to solve for x:
14x/14 ≥ 25/14
x ≥ 25/14
Now, let's analyze the answer choices to determine which values for x make the inequality true:
Option 1: x > -100
This answer choice is not directly supported by the inequality. We can't determine if it's true or false based on the information given.
Option 2: x ≤ 100
This answer choice doesn't satisfy the solution x ≥ 25/14 that we obtained from solving the inequality. Therefore, this is not the correct answer.
Option 3: x ≥ -100
This answer choice satisfies the solution x ≥ 25/14. Since -100 is less than 25/14, it falls within the range of x that makes the inequality true. Therefore, this is a valid answer.
Option 4: x ≥ 100
This answer choice contradicts the solution x ≥ 25/14. Since 100 is greater than 25/14, it does not fall within the range of x that makes the inequality true. Therefore, this is not the correct answer.
Based on the analysis, the correct answer is x ≥ -100.