Solve for $m$.
$7 m=3+4 m$
A. $m=\frac{3}{11}$
B. $m=-7$
C. $m=-\frac{5}{4}$
D. $m=1
Answer (2)
Subtract 4 m from both sides: 7 m − 4 m = 3 + 4 m − 4 m .
Simplify: 3 m = 3 .
Divide both sides by 3: 3 3 m = 3 3 .
Solve for m : m = 1 . The answer is 1 .
Explanation
Understanding the Problem We are given the equation 7 m = 3 + 4 m . Our goal is to isolate m on one side of the equation to find its value.
Isolating the m term First, we subtract 4 m from both sides of the equation to group the m terms together:
7 m − 4 m = 3 + 4 m − 4 m
Simplifying the equation This simplifies to:
3 m = 3
Solving for m Now, we divide both sides of the equation by 3 to solve for m :
3 3 m = 3 3
Final Answer This simplifies to:
m = 1
So, the solution is m = 1 . Therefore, the correct answer is D.
Examples
Understanding linear equations like this is crucial in many real-world scenarios. For example, imagine you're running a small business. You have a fixed cost of $3 (like rent) and a variable cost of $4 per item you sell. If you sell each item for $7, this equation helps you determine how many items you need to sell to break even. In this case, you need to sell 1 item to cover your costs. Linear equations are fundamental in business, economics, and everyday problem-solving.
The solution to the equation 7 m = 3 + 4 m is m = 1 . Thus, the correct choice is D. By isolating m step-by-step, we arrive at this answer.
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