A student evaluates the expressions 3x + 3 and 2x+6 at several different values of x. The student claims, "The value of the expression 3+3 is always greater than the value of the expression 2x +6."
Which value of x can be used to show that the student's claim is false?
O A. 2
O B. 4
O c. 6
O D. 8
A. 2
Oh, the poor student and their misguided claim! Let me put on my big, red clown nose and explain why their claim is false.
Let's evaluate the expression 3x + 3 for each value of x:
For x = 2:
3(2) + 3 = 9
For x = 4:
3(4) + 3 = 15
For x = 6:
3(6) + 3 = 21
For x = 8:
3(8) + 3 = 27
Now let's evaluate the expression 2x + 6 for the same values of x:
For x = 2:
2(2) + 6 = 10
For x = 4:
2(4) + 6 = 14
For x = 6:
2(6) + 6 = 18
For x = 8:
2(8) + 6 = 22
Oh, look at that! For x = 8, the value of the expression 3x + 3 (which is 27) is NOT greater than the value of the expression 2x + 6 (which is 22). So, the correct answer is D. 8.
Remember, students, when it comes to claims, it's always good to check your math before making bold statements. Don't clown around with your evaluations!
To evaluate the student's claim, we need to compare the values of the expressions 3x + 3 and 2x + 6 for different values of x.
Let's substitute each answer choice into the expressions and compare the results:
A. For x = 2:
3x + 3 = 3(2) + 3 = 6 + 3 = 9
2x + 6 = 2(2) + 6 = 4 + 6 = 10
B. For x = 4:
3x + 3 = 3(4) + 3 = 12 + 3 = 15
2x + 6 = 2(4) + 6 = 8 + 6 = 14
C. For x = 6:
3x + 3 = 3(6) + 3 = 18 + 3 = 21
2x + 6 = 2(6) + 6 = 12 + 6 = 18
D. For x = 8:
3x + 3 = 3(8) + 3 = 24 + 3 = 27
2x + 6 = 2(8) + 6 = 16 + 6 = 22
So, by substituting the values, we see that for x = 4, the expression 2x + 6 is greater than the expression 3x + 3. Therefore, the answer is B. 4. This value of x shows that the student's claim is false.
To determine which value of x can be used to show that the student's claim is false, we need to compare the values of the expressions 3x + 3 and 2x + 6 for different values of x.
Let's evaluate the expressions for each given option:
Option A: x = 2
Expression 3x + 3 = 3(2) + 3 = 6 + 3 = 9
Expression 2x + 6 = 2(2) + 6 = 4 + 6 = 10
Option B: x = 4
Expression 3x + 3 = 3(4) + 3 = 12 + 3 = 15
Expression 2x + 6 = 2(4) + 6 = 8 + 6 = 14
Option C: x = 6
Expression 3x + 3 = 3(6) + 3 = 18 + 3 = 21
Expression 2x + 6 = 2(6) + 6 = 12 + 6 = 18
Option D: x = 8
Expression 3x + 3 = 3(8) + 3 = 24 + 3 = 27
Expression 2x + 6 = 2(8) + 6 = 16 + 6 = 22
Looking at the results, we can see that for option B (x = 4), the value of the expression 3x + 3 is 15, which is greater than the value of the expression 2x + 6, which is 14. Therefore, option B can be used to show that the student's claim is false.
Hence, the answer is option B.