Solve the equation:

$-x+8+3x=x-6$

To solve the equation − x + 8 + 3 x = x − 6 , we simplify both sides to isolate x . After combining like terms and rearranging, we find that x = − 14 , which is verified by substituting back into the original equation. Therefore, the solution is x = − 14 .
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Answered by Anonymous | 2025-07-04

Combine like terms on the left side of the equation: − x + 3 x + 8 = 2 x + 8 .
Rewrite the equation: 2 x + 8 = x − 6 .
Subtract x from both sides: x + 8 = − 6 .
Subtract 8 from both sides to solve for x : x = − 14 . The final answer is − 14 ​ .

Explanation

Understanding the Problem We are given the equation − x + 8 + 3 x = x − 6 and asked to solve for x . Our goal is to isolate x on one side of the equation.

Simplifying the Left Side First, let's simplify the left side of the equation by combining like terms: − x + 3 x + 8 = 2 x + 8

Rewriting the Equation Now, the equation becomes: 2 x + 8 = x − 6

Subtracting x from Both Sides Next, subtract x from both sides of the equation to get all the x terms on one side: 2 x − x + 8 = x − x − 6 x + 8 = − 6

Isolating x Now, subtract 8 from both sides to isolate x :
x + 8 − 8 = − 6 − 8 x = − 14

Verification To verify the solution, substitute x = − 14 back into the original equation: − ( − 14 ) + 8 + 3 ( − 14 ) = − 14 − 6 14 + 8 − 42 = − 20 22 − 42 = − 20 − 20 = − 20 Since the equation holds true, the solution is correct.

Final Answer Therefore, the solution to the equation − x + 8 + 3 x = x − 6 is x = − 14 .


Examples
Imagine you're managing a small business and tracking your expenses and income. This equation is similar to balancing your accounts where 'x' could represent an unknown expense. By solving for 'x', you can determine the missing value to ensure your budget balances correctly. This kind of algebraic problem-solving is crucial for financial planning and maintaining accurate records in various real-life scenarios.

Answered by GinnyAnswer | 2025-07-04