Yvonne needs to compare two expressions 13(9x + 6)
and −(3x−10)+6(x−1)
. She needs to know if one expression is greater than the other for all values of x. Which statement accurately describes the relationship between the two expressions.
Responses
The value of 13(9x + 6)
is always less than the value of −(3x−10)+6(x−1)
.
The value of 13(9x + 6)
is always less than the value of negative open paren 3 x minus 10 close paren plus 6 times open paren x minus 1 close paren.
The value of 13(9x + 6)
is always greater than the value of −(3x−10)+6(x−1)
.
The value of 13(9x + 6)
is always greater than the value of negative open paren 3 x minus 10 close paren plus 6 times open paren x minus 1 close paren.
The value of 13(9x + 6)
is always equal to the value of −(3x−10)+6(x−1)
.
The value of 13(9x + 6)
is always equal to the value of negative open paren 3 x minus 10 close paren plus 6 times open paren x minus 1 close paren.
The value of 13(9x + 6)
is sometimes greater than and sometimes less than the value of −(3x−10)+6(x−1)
.
The value of 13(9x + 6) is sometimes greater than and sometimes less than the value of −(3x−10)+6(x−1).
The statement that accurately describes the relationship between the two expressions is:
The value of 13(9x + 6) is sometimes greater than and sometimes less than the value of −(3x−10)+6(x−1).
To compare the expressions 13(9x + 6) and -(3x - 10) + 6(x - 1), we need to simplify and evaluate them.
To simplify the first expression, we distribute the 13 to both terms inside the parentheses:
13(9x + 6) = 117x + 78
To simplify the second expression, we distribute the -1 and 6 to the terms inside the parentheses:
-(3x - 10) + 6(x - 1) = -3x + 10 + 6x - 6 = 3x + 4
Now we can compare the two expressions.
It is clear that the coefficient of x in the first expression (117x + 78) is greater than the coefficient of x in the second expression (3x + 4). This suggests that the first expression (13(9x + 6)) will be greater than the second expression (-(3x - 10) + 6(x - 1)) for certain values of x.
However, we cannot definitively say that one expression is always greater than the other for all values of x without knowing the specific range of x. Therefore, the statement "The value of 13(9x + 6) is sometimes greater than and sometimes less than the value of -(3x - 10) + 6(x - 1)" accurately describes the relationship between the two expressions.