Which could be a first step in solving the equation
1/4x + 1/2 = 3/4x in an efficient way? Select two answers.
A. Multiply by 4 on both sides***
B. Multiply by 2x on both sides
C. Subtract 1/4x from both sides
D. Add 1/2 to both sides***
A ... yes
D ... no
To solve the equation 1/4x + 1/2 = 3/4x efficiently, you can follow these steps:
1. Eliminate the fractions by multiplying every term by the least common denominator (LCD) of the fractions involved. The LCD in this case is 4, so you can multiply by 4 on both sides (option A) to eliminate the fractions.
After multiplying by 4, the equation becomes:
4 * (1/4x) + 4 * (1/2) = 4 * (3/4x)
Simplifying the equation gives:
1x + 2 = 3x
2. Now that the equation does not contain any fractions, your next step is to isolate the x variable on one side. You can do this by subtracting x from both sides to move all terms with x to one side (option C).
Subtracting x from both sides gives:
1x - 3x + 2 = 0
3. Combine like terms and simplify the equation:
-2x + 2 = 0
4. Finally, isolate the x term by subtracting 2 from both sides (option D) and solve for x:
-2x + 2 - 2 = 0 - 2
-2x = -2
Divide both sides by -2:
x = 1
So, the efficient first steps to solve the equation 1/4x + 1/2 = 3/4x are to multiply by 4 on both sides (option A) to eliminate the fractions, and then subtract 1/4x from both sides (option C) to isolate the x term.