To solve this problem, we need to simplify both expressions and compare them.
The first expression, 1/3(9x + 6), can be simplified by distributing the 1/3 to both terms inside the parentheses: (1/3) * 9x + (1/3) * 6. This gives us 3x + 2.
The second expression, -(3x - 10) + 6(x - 1), can be simplified by distributing the -1 and 6 to the terms inside the parentheses: -3x + 10 + 6x - 6. Combining like terms, this gives us 3x + 4.
Comparing the simplified expressions, we have 3x + 2 versus 3x + 4.
These expressions have the same coefficient for x, which means that the value of the expression will only depend on the constant term.
Since 2 is always less than 4, no matter the value of x, we can conclude that:
A. The value of 1/3 (9x + 6) is always less than the value of - (3x - 10) + 6(x - 1).
Yvonne needs to compare two expressions 1/3(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.
A. The value of 1/3 (9x + 6) is always less than the value of - (3x - 10) + 6(x - 1)
B. The value of 1/3 (9x + 6) is always greater than the value of - (3x - 10) + 6(x - 1)
C. The value of 1/3 (9x + 6) is always equal to the value of - (3x - 10) + 6(x - 1)
D. The value of 1/3 (9x + 6) is sometimes greater than and sometimes less than the value of - (3x - 10) + 6(x - 1)
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