How do you solve 9−2x=35?
The Correct Answer and Explanation is:
To solve the equation (9 – 2x = 35), we need to isolate the variable (x) step-by-step. Here’s a breakdown of the solution:
Step-by-Step Solution
- Start with the original equation:
[
9 – 2x = 35
] - Isolate the term with the variable:
To make it easier to solve for (x), we want to move the constant (9) to the other side of the equation. We can do this by subtracting 9 from both sides:
[
9 – 2x – 9 = 35 – 9
]
This simplifies to:
[
-2x = 26
] - Divide by the coefficient of (x):
Now, we have (-2x) on the left side. To isolate (x), we need to divide both sides by (-2):
[
x = \frac{26}{-2}
]
Simplifying the right side gives:
[
x = -13
]
Thus, the solution is:
[
x = -13
]
Explanation of the Steps
The goal in solving linear equations like (9 – 2x = 35) is to isolate the variable, in this case (x), on one side of the equation. Here’s a breakdown of why each step works:
- Subtracting 9 from both sides helps eliminate the constant term on the left side, simplifying the equation. In solving equations, whatever operation we perform on one side, we must also perform on the other to maintain equality.
- Dividing by (-2) isolates (x). The (-2) is the coefficient of (x), so dividing both sides by (-2) “cancels out” this factor, leaving (x) alone.
- Checking the solution: To verify, substitute (x = -13) back into the original equation:
[
9 – 2(-13) = 9 + 26 = 35
]
Since both sides are equal, our solution (x = -13) is correct.
This approach works for any linear equation: by isolating terms involving (x), we can gradually simplify to solve for the variable.