Solve for e 9e + 4 = − 5e + 14 + 13e 9e + 4 = -5e + 14 + 13e
The Correct Answer and Explanation is:
To solve for ( e ) in the equation:
[
9e + 4 = -5e + 14 + 13e
]
Step 1: Simplify both sides of the equation.
On the right-hand side, combine the like terms (-5e) and (13e):
[
9e + 4 = ( -5e + 13e) + 14
]
[
9e + 4 = 8e + 14
]
Now, the equation is:
[
9e + 4 = 8e + 14
]
Step 2: Move the terms involving ( e ) to one side of the equation.
To eliminate ( 8e ) from the right side, subtract ( 8e ) from both sides of the equation:
[
9e – 8e + 4 = 8e – 8e + 14
]
[
e + 4 = 14
]
Step 3: Move the constant terms to the other side.
Now, subtract ( 4 ) from both sides of the equation:
[
e + 4 – 4 = 14 – 4
]
[
e = 10
]
So, the solution is ( e = 10 ).
Explanation:
In this problem, we are solving a linear equation involving the variable ( e ). To solve for ( e ), we follow the basic algebraic steps of simplifying and isolating the variable.
- Simplification: First, we combine like terms, especially the terms with ( e ) on both sides of the equation.
- Isolating the variable: We then move all terms involving ( e ) to one side and constant terms to the other side to simplify the equation further.
- Final step: By subtracting and adding appropriate terms, we isolate ( e ) on one side of the equation, allowing us to solve for its value.
This method is called solving a linear equation, and it ensures that we find the correct value for the variable by maintaining the equality of both sides of the equation.