A student evaluates the expressions 3x + 3 and 2x + 6 at several different values of . The student claims, "The value of the expression 3x + 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?
x = -3
To show that the student's claim is false, we need to find a value of x where the expression 3x + 3 is not greater than the expression 2x + 6.
Let's find this value by setting the two expressions equal to each other and solving for x:
3x + 3 = 2x + 6
Subtracting 2x from both sides:
x + 3 = 6
Subtracting 3 from both sides:
x = 3
So, when x = 3, both expressions are equal:
3(3) + 3 = 2(3) + 6
9 + 3 = 6 + 6
12 = 12
Therefore, the value x = 3 can be used to show that the student's claim is false because at this value, both expressions are equal, not greater.
To determine the value of x that can be used to show that the student's claim is false, we need to find a value of x where the expression 3x + 3 is not greater than the expression 2x + 6.
First, let's compare the two expressions:
Expression 1: 3x + 3
Expression 2: 2x + 6
To find the value of x that makes the two expressions equal, we can set them equal to each other:
3x + 3 = 2x + 6
Next, we can solve this equation for x:
3x - 2x = 6 - 3
x = 3
Now, substituting x = 3 into the expressions:
Expression 1: 3(3) + 3 = 9 + 3 = 12
Expression 2: 2(3) + 6 = 6 + 6 = 12
As you can see, when x = 3, the values of the two expressions are equal.
To show that the student's claim is false, we need to find a value of x that makes the expression 3x + 3 less than the expression 2x + 6.
Let's choose x = 2:
Expression 1: 3(2) + 3 = 6 + 3 = 9
Expression 2: 2(2) + 6 = 4 + 6 = 10
When x = 2, the value of the expression 3x + 3 is not greater than the value of the expression 2x + 6. Therefore, x = 2 can be used to show that the student's claim is false.