Which expression is equivalent to 2/3(4x - 9)?
A
8x - 18
8 x - 18 3
B
8x - 9
3
8 x - 9 3
C
8 (x + 18)
3
8 ( x + 18) 3
D
8 (x - 12)
3
The correct expression that is equivalent to 2/3(4x - 9) is 8x - 6.
The correct expression that is equivalent to 2/3(4x - 9) is:
A) 8x - 18
To determine which expression is equivalent to 2/3(4x - 9), we need to apply the distributive property.
The distributive property states that when a number (in this case, 2/3) is multiplied by a term inside parentheses (in this case, 4x - 9), we distribute the number to every term inside the parentheses.
So, let's apply the distributive property to each option and simplify:
A) 8x - 18: This option distributes 2/3 to every term inside the parentheses: (2/3 * 4x) - (2/3 * 9) = (8/3)x - 6.
As we can see, this option is not equivalent to 2/3(4x - 9) because it doesn't simplify to the same expression.
B) 8x - 9: This option distributes 2/3 to every term inside the parentheses: (2/3 * 4x) - (2/3 * (-9)) = (8/3)x + 6.
As we can see, this option is not equivalent to 2/3(4x - 9) because it doesn't simplify to the same expression.
C) 8(x + 18)/3: This option also distributes 2/3 to every term inside the parentheses: (2/3 * 8) * (x + 18) = (16/3)(x + 18).
As we can see, this option is not equivalent to 2/3(4x - 9) because it doesn't simplify to the same expression.
D) 8(x - 12)/3: This option distributes 2/3 to every term inside the parentheses: (2/3 * 8) * (x - 12) = (16/3)(x - 12).
As we can see, this option is equivalent to 2/3(4x - 9) because both expressions simplify to (16/3)(x - 12).
Therefore, the correct answer is option D) 8(x - 12)/3.