Answer:
To eliminate the fractions in the equation -3/4m - 1/2 = 2 + 1/4m, you can multiply each term of the equation by the least common multiple (LCM) of the denominators, which is 4.
So, you would multiply every term by 4:
4 * (-3/4m) - 4 * (1/2) = 4 * 2 + 4 * (1/4m)
This simplifies to:
-3m - 2 = 8 + m
Now, you can solve for 'm':
-3m - m = 8 + 2
-4m = 10
m = -10/4
Simplifying further, m = -5/2.
So, the answer to your question is C. You can multiply each term of the equation by 4 to eliminate the fractions.
Explanation:
Certainly, here's a step-by-step explanation of how to eliminate the fractions and solve the equation -3/4m - 1/2 = 2 + 1/4m:
Step 1: Identify the Fractions
Identify the fractions in the equation. In this case, you have two fractions: -3/4m and -1/2 on the left side and 1/4m on the right side.
Step 2: Find the Least Common Multiple (LCM)
To eliminate fractions, you need to find the Least Common Multiple (LCM) of the denominators. In this equation, the denominators are 4 and 2. The LCM of 4 and 2 is 4.
Step 3: Multiply Each Term by the LCM
Now, multiply each term of the equation by the LCM, which is 4:
4 * (-3/4m) - 4 * (1/2) = 4 * (2) + 4 * (1/4m)
Step 4: Distribute the Multiplication
Distribute the 4 to each term:
(-3/4m) * 4 - (1/2) * 4 = 2 * 4 + (1/4m) * 4
Step 5: Simplify Each Term
Now, simplify each term:
-3m - 2 = 8 + m
Step 6: Isolate 'm' on One Side
To solve for 'm,' you want to isolate 'm' on one side of the equation. Start by moving 'm' terms to the left side by adding 'm' to both sides:
-3m - m - 2 = 8
Now, combine the 'm' terms on the left side:
-4m - 2 = 8
Step 7: Move Constant Terms to the Right Side
To isolate '-4m' on the left side, move the constant term (-2) to the right side by adding 2 to both sides:
-4m = 8 + 2
-4m = 10
Step 8: Solve for 'm'
Finally, to find the value of 'm,' divide both sides by -4:
m = 10 / -4
Simplify the fraction:
m = -5/2
So, the solution to the equation is m = -5/2.