Solving the Equation -3x - 25x - 68 - 2x -2 - 2x - 10 - 20
In this article, we will explore the process of solving a linear equation involving multiple terms. The equation in question is -3x - 25x - 68 - 2x -2 - 2x - 10 - 20. Let's break down the solution step-by-step to understand the methods used in algebra.
Step-by-Step Solution
First, let's simplify the equation by combining like terms on both sides.
Left Side Simplification
-3x - 25x - 68 - 2x
Combining the x-terms and constants:
-3x - 25x - 2x -3
Simplifying the constants:
-68
Right Side Simplification
-2 - 2x - 10 - 20
Combining the x-terms and constants:
-2x
Simplifying the constants:
-2 - 10 - 20 -32
Final Equation
Thus, the equation simplifies to:
-3 - 68 -2x - 32
Solving for x
To solve for x, we will place all terms involving x on one side and all constants on the other side.
Isolating x
User Solution 1:
-3 - 2x -32 68
-32x 36
x -36 / 32 -9 / 8
User Solution 2:
-3 - 2x - 68 -2x - 32
-32x 36
x -36 / 32 -9 / 8
Common Solution
After re-examining the equation, it seems there was a misinterpretation of the equation. Let's solve the equation correctly by grouping terms.
Correct Grouping
-3x - 25x - 68 - 2x -2 - 2x - 10 - 20
-3 - 68 -2x - 32
-3 2x -32 68
-28x 36
x -36 / 28 -9 / 7
However, considering the given solutions, let's analyze the correct steps and ensure the answer matches one of the previous solutions.
Correct Solution
-3x - 25x - 68 - 2x -2 - 2x - 10 - 20
-3 - 68 -2x - 32
-3 2x -32 68
-28x 36
x -36 / 28 -9 / 7
But simplifying, we get:
x 1
Key Takeaways
The primary steps in solving this equation are:
Combine like terms on both sides of the equation. Maintain the balance of the equation by performing the same operations on both sides. Solve for x by isolating it on one side of the equation.Understanding these steps helps in solving similar linear equations.
Conclusion
The final value of x is 1. This detailed process ensures a clear and thorough understanding of solving linear algebraic equations.