Find the value of “m” if 5m – 7 = 4m – 9
A. -2
B. -1
C. 0
D. 1
Explanation:
To find the value of “m” in the equation 5m – 7 = 4m – 9, we need to isolate the variable on one side of the equation. We can do this by subtracting 4m from both sides of the equation:
5m – 7 – 4m = 4m – 9 – 4m
m – 7 = -9
Next, we can add 7 to both sides of the equation:
m – 7 + 7 = -9 + 7
m = -2
Therefore, the value of “m” in the equation 5m – 7 = 4m – 9 is -2.
Solving Linear Equations in One Variable: Steps and Examples
Linear equations in one variable are equations that can be written in the form ax + b = c, where “a”, “b”, and “c” are constants and “x” is a variable. Solving linear equations in one variable involves finding the value of the variable that makes the equation true.
Here are the steps to solve a linear equation in one variable:
- Step 1: Simplify both sides of the equation by combining like terms if necessary.
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Step 2: Isolate the variable on one side of the equation by using inverse operations.
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Step 3: Check your answer by substituting the value of the variable back into the original equation.
Let’s take an example to understand this better. Consider the equation 2x – 5 = 7. To solve this equation, we need to isolate the variable “x” on one side of the equation. We can do this by adding 5 to both sides of the equation:
2x – 5 + 5 = 7 + 5
2x = 12
Next, we can divide both sides of the equation by 2:
2x/2 = 12/2
x = 6
Therefore, the solution to the equation 2x – 5 = 7 is x = 6.
It is important to note that some linear equations may not have a solution, while others may have infinitely many solutions. For example, the equation 2x + 4 = 2(x + 2) has no solution, while the equation x + 3 = x + 3 has infinitely many solutions.
In conclusion, solving linear equations in one variable involves following a few simple steps to find the value of the variable that makes the equation true. Understanding this concept is essential for solving problems in algebra and other areas of mathematics.