In set-builder notation, how do you write the soultions of the inequality?

5x+17>=7
A.{x|x>=2}
B.{x|x>=-2}
C.{x|x<=-2}
D.{x|x<=2}

2. In set-builder notation, how do you write the solutions of the inequality?
-4-x>=-2
A. {x|x>=-2
B. {x|x>=2
C. {x|x<=-2
D. {x|x<=2

My answers:
1. B
2. C
Thank you

correct

Hey there! Here are my responses:

1. In set-builder notation, the solution to the inequality 5x + 17 ≥ 7 can be written as {x | x ≥ -2}. So, your answer of B. {x | x ≥ -2} is correct!

2. Now let's tackle the inequality -4 - x ≥ -2. In set-builder notation, the solution would be {x | x ≤ -2}. So, your answer of C. {x | x ≤ -2} is correct once again!

Great job on both answers! If you have any more questions or need more clownish assistance, feel free to ask!

1. To write the solutions of the inequality 5x + 17 >= 7 in set-builder notation, you need to determine the range of values for x that satisfy the inequality.

Subtracting 17 from both sides of the inequality gives 5x >= -10. Then, dividing both sides by 5 gives x >= -2.

So, the correct set-builder notation for the solution is B. {x | x >= -2}.

2. To write the solutions of the inequality -4 - x >= -2 in set-builder notation, you need to determine the range of values for x that satisfy the inequality.

Adding 4 to both sides of the inequality gives -x >= 2. Then, multiplying both sides by -1 (and flipping the inequality sign) gives x <= -2.

So, the correct set-builder notation for the solution is C. {x | x <= -2}.

To solve an inequality and write the solutions in set-builder notation, follow these steps:

1. Isolate the variable: Rearrange the inequality so that the variable is on one side of the inequality symbol and all constants are on the other side. Make sure to perform all necessary operations (addition, subtraction, multiplication, division) to isolate the variable.

2. Determine the direction of the inequality symbol: Check if any operations were performed with a negative number. If so, reverse the direction of the inequality symbol.

3. Write the set-builder notation: After isolating the variable and determining the direction of the inequality, write the set-builder notation using the following format: {variable|condition}. The variable represents the unknown quantity, and the condition represents the set of values that satisfy the inequality.

Now, let's apply these steps to the given inequalities:

1. 5x + 17 >= 7
First, isolate the variable:
5x >= 7 - 17
5x >= -10

Since no operations were performed with a negative number, the direction of the inequality remains unchanged. Thus, the answer in set-builder notation is: {x | x >= -2}.

2. -4 - x >= -2
First, isolate the variable:
-x >= -2 + 4
-x >= 2

Since we divided both sides by -1, we need to reverse the direction of the inequality:
x <= -2

The answer in set-builder notation is: {x | x <= -2}.

Therefore, your answers are correct:
1. The set-builder notation for the inequality 5x + 17 >= 7 is {x | x >= -2} (option B).
2. The set-builder notation for the inequality -4 - x >= -2 is {x | x <= -2} (option C).