Which sum or difference is equivalent to the following expression? 2x+3 over 4 A) x/2 + 3/4 B) x/2 - 3/4 C) 3x/4 + 3/4 D) 8x + 24
The equivalent sum or difference to the expression 2x + 3/4 is option A) x/2 + 3/4.
To find an equivalent sum or difference for the expression (2x + 3) / 4, you need to simplify it further. Here's how you can do it step-by-step:
Step 1: Begin by distributing the 1/4 to both terms inside the parentheses:
(2/4)x + (3/4)
Step 2: Simplify the fraction 2/4 by dividing the numerator and denominator by their greatest common divisor, which is 2:
1/2 * x + 3/4
Step 3: The expression is now simplified to:
x/2 + 3/4
Therefore, the sum or difference that is equivalent to (2x + 3) / 4 is option A) x/2 + 3/4.
To find the equivalent sum or difference, we need to simplify the expression 2x + 3/4.
First, let's start by expressing the expression as two separate terms:
2x + 3/4 = 2x + (3/4)
Now, let's find the common denominator for the terms. In this case, the common denominator is 4 because the second term already has a denominator of 4:
2x + (3/4) = (2x * 4/4) + (3/4)
Next, we can add the numerators of the two terms since they have the same denominator:
(2x * 4/4) + (3/4) = (8x + 3)/4
Therefore, the expression 2x + 3/4 is equivalent to the sum (8x + 3)/4.
Comparing the available options:
A) x/2 + 3/4 - This does not match our simplified expression.
B) x/2 - 3/4 - This does not match our simplified expression.
C) 3x/4 + 3/4 - This does not match our simplified expression.
D) 8x + 24 - This does not match our simplified expression.
None of the given options match the equivalent sum or difference of the expression 2x + 3/4, which is (8x + 3)/4.