Which expression is equivalent to 2/3x + 1?
A- 1/3(2x+3)
B- 2/3(2x+3)
C- 2/3 (3x+2)
D- 2/3(3x+1)
The correct answer is C- 2/3 (3x+2)
To find which expression is equivalent to 2/3x + 1, we can start by factoring out the common factor of x from the expression 2/3x:
2/3x + 1 = (2/3)x + 1
So now we have the expression as (2/3)x + 1.
Now let's compare this expression to the answer choices:
A- 1/3(2x+3)
B- 2/3(2x+3)
C- 2/3 (3x+2)
D- 2/3(3x+1)
By comparing the expressions, we can see that option B, 2/3(2x+3), is the equivalent expression to 2/3x + 1.
To determine which expression is equivalent to 2/3x + 1, we need to distribute the 2/3 to the terms inside the parentheses.
Let's go through each option and distribute 2/3:
A) 1/3(2x + 3) = (1/3) * 2x + (1/3) * 3 = 2/3x + 1
B) 2/3(2x + 3) = (2/3) * 2x + (2/3) * 3 = 4/3x + 2
C) 2/3(3x + 2) = (2/3) * 3x + (2/3) * 2 = 2x + 4/3
D) 2/3(3x + 1) = (2/3) * 3x + (2/3) * 1 = 2x + 2/3
Out of these options, the only expression that is equivalent to 2/3x + 1 is A) 1/3(2x + 3).