Solve for x. x + 5 = 2x
The Correct Answer and Explanation is :
To solve the equation ( x + 5 = 2x ), follow these steps:
Step 1: Understand the equation
The equation is a simple linear equation involving the variable ( x ). We need to isolate ( x ) on one side of the equation to find its value.
Step 2: Subtract ( x ) from both sides
We want to get all terms involving ( x ) on one side of the equation. To do this, subtract ( x ) from both sides:
[
x + 5 – x = 2x – x
]
Simplifying both sides:
[
5 = x
]
Step 3: Interpret the result
After simplifying the equation, we see that ( x = 5 ). This is the solution to the equation.
Step 4: Verify the solution
To verify that our solution is correct, substitute ( x = 5 ) back into the original equation:
[
x + 5 = 2x
]
Substituting ( x = 5 ):
[
5 + 5 = 2(5)
]
[
10 = 10
]
Since both sides are equal, the solution ( x = 5 ) is correct.
Explanation of the process
In solving this equation, we used basic algebraic principles. The goal in any linear equation is to isolate the variable (in this case, ( x )) on one side of the equation. By subtracting ( x ) from both sides, we eliminated the variable on the left side, allowing us to find the value of ( x ).
This type of equation is commonly encountered in algebra and is important for solving more complex equations and systems of equations. It illustrates the fundamental principle of maintaining equality: whatever operation you perform on one side of the equation must also be performed on the other side.
In summary, the solution to the equation ( x + 5 = 2x ) is ( x = 5 ). This result was verified by substituting it back into the original equation to ensure the sides remain balanced.