Solve the equation.
$-x+8+3 x=x-6$
Answer (1)
Combine like terms: − x + 3 x + 8 = 2 x + 8 .
Rewrite the equation: 2 x + 8 = x − 6 .
Isolate x : 2 x − x = − 6 − 8 .
Solve for x : x = − 14 . The final answer is − 14 .
Explanation
Analyze the equation First, let's analyze the given equation: − x + 8 + 3 x = x − 6 Our goal is to isolate x on one side of the equation to find its value.
Combine like terms Combine the like terms on the left side of the equation: − x + 3 x + 8 = x − 6 2 x + 8 = x − 6
Isolate x term Subtract x from both sides of the equation to get the x terms on one side: 2 x + 8 − x = x − 6 − x x + 8 = − 6
Solve for x Subtract 8 from both sides of the equation to isolate x :
x + 8 − 8 = − 6 − 8 x = − 14
Final Answer Therefore, the solution to the equation is x = − 14 .
Examples
In real-world scenarios, solving linear equations like this can help determine unknown quantities. For example, if you know that a certain amount of money plus a fixed cost equals another known amount, you can use a linear equation to find the initial amount of money. Suppose you have a balance and after adding $8 and tripling your initial balance, you have the same amount as if you started with the initial balance and lost $6. This equation helps you find the initial balance.
