Solve for x.
9(x + 1) = 25 + x
bo
x=2
x=3
X=4
x=5
The Correct Answer and Explanation is :
To solve the equation ( 9(x + 1) = 25 + x ), let’s follow the steps systematically:
Step 1: Expand the equation
First, distribute the ( 9 ) on the left side to both terms inside the parentheses:
[
9(x + 1) = 9x + 9
]
So, the equation becomes:
[
9x + 9 = 25 + x
]
Step 2: Isolate the variable terms
Now, to isolate the variable ( x ), let’s get all the terms involving ( x ) on one side of the equation and the constant terms on the other side.
First, subtract ( x ) from both sides to eliminate ( x ) from the right side:
[
9x + 9 – x = 25 + x – x
]
This simplifies to:
[
8x + 9 = 25
]
Step 3: Move constant terms
Next, subtract ( 9 ) from both sides to isolate the term with ( x ):
[
8x + 9 – 9 = 25 – 9
]
This simplifies to:
[
8x = 16
]
Step 4: Solve for ( x )
Now, divide both sides by ( 8 ) to solve for ( x ):
[
\frac{8x}{8} = \frac{16}{8}
]
This simplifies to:
[
x = 2
]
Conclusion:
The correct value of ( x ) is 2.
Explanation:
The equation ( 9(x + 1) = 25 + x ) is a linear equation where the goal is to isolate the variable ( x ). By expanding the left side, we then grouped the terms involving ( x ) and the constant terms, eventually isolating ( x ) on one side of the equation. This approach shows how we systematically simplify both sides of the equation to solve for the unknown value of ( x ).
Thus, the correct answer is ( x = 2 ).