m = 10x – x solve for x
The Correct Answer and Explanation is:
Solution:
We are given the expression: m=10x−xm = 10x – x
Step 1: Simplify the right-hand side
10x−x=9x10x – x = 9x
So the equation becomes: m=9xm = 9x
Step 2: Solve for xx
x=m9x = \frac{m}{9}
Final Answer:
x=m9x = \frac{m}{9}
300-Word Explanation:
This problem is a basic algebraic equation where the goal is to isolate the variable xx. The equation given is: m=10x−xm = 10x – x
To solve it, we first need to simplify the expression on the right-hand side. The terms 10x10x and −x-x are like terms because they both contain the variable xx. When combining like terms in algebra, we perform simple arithmetic on their coefficients. In this case: 10x−x=(10−1)x=9x10x – x = (10 – 1)x = 9x
So the equation becomes: m=9xm = 9x
Now, to isolate xx, we want to “undo” the multiplication. Since xx is being multiplied by 9, we perform the inverse operation: division. We divide both sides of the equation by 9: x=m9x = \frac{m}{9}
This is the final answer. It tells us the value of xx in terms of mm. It means that whatever value mm has, xx will be one-ninth of that value. For example, if m=27m = 27, then: x=279=3x = \frac{27}{9} = 3
This approach demonstrates a fundamental algebraic principle: simplify expressions first, then isolate the variable using inverse operations. This same technique applies to a wide range of algebra problems and forms the foundation for solving equations. Understanding how to manipulate variables and constants symbolically is key to mastering algebra and higher mathematics.
