Solve the equation
$-9 x+1=-x+17$
Answer (2)
Isolate x terms on one side and constants on the other: − 9 x + 1 = − x + 17 becomes − 8 x = 16 .
Divide by -8 to solve for x: x = − 8 16 .
Simplify: x = − 2 .
The solution to the equation is − 2 .
Explanation
Problem Analysis We are given the equation − 9 x + 1 = − x + 17 and a set of possible solutions x = − 8 , − 2 , 2 , 6 . Our goal is to find the correct solution from the given options. We can solve this by either solving the equation directly or by substituting each of the given values into the equation to see which one satisfies it. Let's solve the equation directly.
Solving the Equation To solve the equation − 9 x + 1 = − x + 17 , we first want to isolate the terms with x on one side and the constant terms on the other side. We can add 9 x to both sides of the equation to get: 1 = 8 x + 17 Next, we subtract 17 from both sides: 1 − 17 = 8 x − 16 = 8 x Finally, we divide both sides by 8 to solve for x :
x = 8 − 16 x = − 2
Checking the Solution Now that we have found the solution x = − 2 , we can check if it is among the given possible solutions. The given possible solutions are x = − 8 , − 2 , 2 , 6 . We see that x = − 2 is indeed one of the given options.
Verification To be absolutely sure, let's substitute x = − 2 into the original equation: − 9 ( − 2 ) + 1 = − ( − 2 ) + 17 18 + 1 = 2 + 17 19 = 19 Since the equation holds true, x = − 2 is the correct solution.
Final Answer Therefore, the solution to the equation − 9 x + 1 = − x + 17 is x = − 2 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and other quantities. For example, if you want to determine how many hours you need to work to earn a certain amount of money, you can set up a linear equation to model the situation. Similarly, if you are planning a road trip and want to calculate the distance you can travel in a certain amount of time, you can use a linear equation to model the relationship between distance, speed, and time. Understanding how to solve linear equations is a fundamental skill that can be applied in many practical situations.
The solution to the equation − 9 x + 1 = − x + 17 is x = − 2 . After solving for x , we also verified the solution by substituting it back into the original equation. Thus, x = − 2 is indeed the correct answer.
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