Simplify and solve this equation: [tex]4 m+9+5 m-12=42[/tex].
A. [tex]m=5[/tex]
B. [tex]m=-5[/tex]
C. [tex]m=-4[/tex]
D. [tex]m=4[/tex]
Answer (1)
Combine like terms: 4 m + 5 m + 9 − 12 = 42 becomes 9 m − 3 = 42 .
Add 3 to both sides: 9 m = 45 .
Divide by 9: m = 5 .
The solution is m = 5 .
Explanation
Analyze the equation Let's solve the equation step-by-step. The given equation is 4 m + 9 + 5 m − 12 = 42 .
Combine like terms First, we combine the like terms on the left side of the equation. We have 4 m and 5 m , which combine to 9 m . We also have 9 and − 12 , which combine to − 3 . So the equation becomes 9 m − 3 = 42 .
Isolate the m term Next, we want to isolate the term with m . To do this, we add 3 to both sides of the equation: 9 m − 3 + 3 = 42 + 3 , which simplifies to 9 m = 45 .
Solve for m Now, we divide both sides of the equation by the coefficient of m , which is 9 . So we have 9 9 m = 9 45 , which simplifies to m = 5 .
Final Answer Therefore, the solution to the equation is m = 5 . Comparing this to the given options, we see that option A is the correct answer.
Examples
Imagine you're balancing a budget. You have some income ( m ) and some expenses. This equation helps you figure out how much income you need to reach a specific financial goal. By simplifying and solving the equation, you determine the exact value of m required to balance your budget and achieve your target.
