Solve for x in the equation: 13x + 7 = 8x + 27
The Correct Answer and Explanation is:
To solve the equation ( 13x + 7 = 8x + 27 ), we will isolate the variable ( x ) by following a series of algebraic steps.
Step 1: Rearrange the equation
First, we want to get all terms involving ( x ) on one side and the constant terms on the other side. We can do this by subtracting ( 8x ) from both sides:
[
13x – 8x + 7 = 27
]
This simplifies to:
[
5x + 7 = 27
]
Step 2: Isolate the variable term
Next, we need to isolate the term with ( x ). We can achieve this by subtracting ( 7 ) from both sides of the equation:
[
5x + 7 – 7 = 27 – 7
]
This results in:
[
5x = 20
]
Step 3: Solve for ( x )
Now, to find the value of ( x ), we divide both sides of the equation by ( 5 ):
[
x = \frac{20}{5}
]
Thus, we find:
[
x = 4
]
Verification
It is always good practice to verify the solution by substituting ( x ) back into the original equation. Let’s substitute ( x = 4 ):
The left side of the equation becomes:
[
13(4) + 7 = 52 + 7 = 59
]
The right side of the equation becomes:
[
8(4) + 27 = 32 + 27 = 59
]
Since both sides are equal (( 59 = 59 )), our solution ( x = 4 ) is confirmed.
Conclusion
The final solution to the equation ( 13x + 7 = 8x + 27 ) is ( x = 4 ). The process involved rearranging the equation, isolating the variable, and performing basic algebraic operations, which are fundamental skills in solving linear equations.