Which could be a first step in solving the equation 1/4x + 1/2 = 3/4x in an efficient way? Select two answers.
multiply by 4 on both sides
multiply by 2x on both sides
subtract 1/4x from both sides
add 1/2 to both sides
The first step in solving the equation 1/4x + 1/2 = 3/4x in an efficient way is to eliminate the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators.
The given equation has denominators of 4, 2, and 4 for the terms 1/4x, 1/2, and 3/4x, respectively. The LCM of these denominators is 4.
Therefore, we can multiply every term in the equation by 4 to eliminate the fractions.
This means the first step is to multiply both sides of the equation by 4:
(4) * (1/4x) + (4) * (1/2) = (4) * (3/4x)
After performing this step, the equation becomes:
1x + 2 = 3x
The second step of solving the equation can be to isolate the variable term, x. This can be done by performing operations such as subtracting or adding terms to both sides of the equation.
Looking at the given options, two correct answers would be:
1. Subtract 1x (or x) from both sides:
1x - 1x + 2 = 3x - 1x
This simplifies to:
2 = 2x
2. Subtract 2 from both sides:
2 - 2 = 2x - 2
This simplifies to:
0 = 2x
These two steps will help simplify the equation and bring it closer to finding the value of x.