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 (2)
Combine like terms: 4 m + 5 m + 9 − 12 = 9 m − 3 .
Rewrite the equation: 9 m − 3 = 42 .
Add 3 to both sides: 9 m = 45 .
Divide by 9: m = 9 45 = 5 . The solution is m = 5 .
Explanation
Understanding the Problem We are given the equation 4 m + 9 + 5 m − 12 = 42 . Our goal is to simplify the equation and solve for the variable m .
Combining Like Terms First, we combine the like terms on the left side of the equation. We have two terms with m : 4 m and 5 m . Adding these gives us 4 m + 5 m = 9 m . We also have two constant terms: 9 and − 12 . Adding these gives us 9 − 12 = − 3 . So, the left side of the equation simplifies to 9 m − 3 .
Isolating the Variable Term Now our equation is 9 m − 3 = 42 . To isolate the term with m , we need to add 3 to both sides of the equation. This gives us 9 m − 3 + 3 = 42 + 3 , which simplifies to 9 m = 45 .
Solving for m Finally, to solve for m , we need to divide both sides of the equation by the coefficient of m , which is 9 . This gives us 9 9 m = 9 45 , which simplifies to m = 5 .
Final Answer Therefore, the solution to the equation is m = 5 .
Examples
Imagine you're buying multiple items at a store. If you buy 4 of one item and 5 of another, and you have some discounts and extra charges, this problem is like figuring out the price of each item if your total bill is $42. By combining the costs of similar items and accounting for the extra charges, you can solve for the individual price.
The equation 4 m + 9 + 5 m − 12 = 42 simplifies to m = 5 after combining like terms and isolating the variable. The chosen answer is option A: m = 5 .
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