How do i solve -(1+7x)-6(-7-x)=36
The Correct Answer and Explanation is :
To solve the equation (- (1 + 7x) – 6(-7 – x) = 36), follow these steps:
Step 1: Simplify both sides of the equation
Start by distributing the negative sign on the left side:
[
- (1 + 7x) = -1 – 7x
]
Next, distribute (-6) in the term (-6(-7 – x)):
[
-6(-7) – 6(-x) = 42 + 6x
]
So, the equation can be rewritten as:
[
-1 – 7x + 42 + 6x = 36
]
Step 2: Combine like terms
Now, combine the constant terms and the (x) terms on the left side:
[
(-1 + 42) + (-7x + 6x) = 36
]
This simplifies to:
[
41 – x = 36
]
Step 3: Isolate the variable (x)
To isolate (x), subtract 41 from both sides:
[
41 – x – 41 = 36 – 41
]
This simplifies to:
[
-x = -5
]
Step 4: Solve for (x)
Now, multiply both sides by (-1) to solve for (x):
[
x = 5
]
Final Answer
Thus, the solution to the equation (- (1 + 7x) – 6(-7 – x) = 36) is:
[
\boxed{5}
]
Explanation of the Steps
- Distributing Negative Signs: The negative signs in the equation indicate that each term inside the parentheses must be changed in sign. This step is crucial for maintaining the equality.
- Combining Like Terms: This simplifies the equation and makes it easier to work with. It reduces complexity by consolidating similar variables and constants.
- Isolating Variables: The goal is to get the variable on one side of the equation by performing operations that will not change the equality.
- Finalizing the Solution: After isolating the variable, it’s essential to present the final answer clearly.
By following these systematic steps, you can solve linear equations effectively and accurately.