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)
you have to pick one
A) 1/3(2x+3)
To find an expression equivalent to 2/3x + 1, you need to distribute the fraction 2/3 to the terms inside the parentheses.
A) 1/3(2x+3) = (2x+3)/3
B) 2/3(2x+3) = (4x+6)/3
C) 2/3(3x+2) = (6x+4)/3
D) 2/3(3x+1) = (6x+2)/3
Comparing the expressions, the equivalent expression is (6x+2)/3, which matches option D. Therefore, the answer is option D.
To determine which expression is equivalent to 2/3x + 1, we need to distribute the 2/3 to the terms inside the brackets and then compare the resulting expression with the given options.
Let's distribute the 2/3 through the expression 2x + 3:
(2/3)(2x + 3) = (2/3) * 2x + (2/3) * 3
= 4/3x + 6/3
= (4x + 6)/3
Now we can compare this with the given options:
A) 1/3(2x + 3) = (2/3x + 1)
This option is not equivalent to 2/3x + 1.
B) 2/3(2x + 3) = (4x + 6)/3
This option matches the expression we derived earlier, so it is equivalent to 2/3x + 1.
C) 2/3(3x + 2) = (6x + 4)/3
This option is not equivalent to 2/3x + 1.
D) 2/3(3x + 1) = (6x + 2)/3
This option is not equivalent to 2/3x + 1.
Therefore, the expression that is equivalent to 2/3x + 1 is option B) 2/3(2x + 3).