Solve the equation.
$-9 x+1=-x+17$
Answer (2)
Add 9 x to both sides: 1 = 8 x + 17 .
Subtract 17 from both sides: − 16 = 8 x .
Divide both sides by 8: x = − 2 .
The solution to the equation is x = − 2 .
Explanation
Understanding the Problem We are given the equation − 9 x + 1 = − x + 17 and asked to solve for x . This is a linear equation, and our goal is to isolate x on one side of the equation.
Isolating x terms To solve the equation, we first want to group the terms with x on one side and the constant terms on the other side. Let's add 9 x to both sides of the equation: − 9 x + 1 + 9 x = − x + 17 + 9 x
1 = 8 x + 17
Isolating the x term Now, subtract 17 from both sides of the equation to isolate the term with x :
1 − 17 = 8 x + 17 − 17 − 16 = 8 x
Solving for x Finally, divide both sides by 8 to solve for x :
8 − 16 = 8 8 x x = − 2
Verification To verify the solution, substitute x = − 2 back into the original equation: − 9 ( − 2 ) + 1 = − ( − 2 ) + 17 18 + 1 = 2 + 17 19 = 19 The equation holds true, so our solution is correct.
Final Answer Therefore, the solution to the equation − 9 x + 1 = − x + 17 is x = − 2 .
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items, determining distances, and modeling relationships between two variables. 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 where the number of hours is the variable, and the hourly wage is the coefficient. Solving the equation will give you the number of hours you need to work.
The solution to the equation − 9 x + 1 = − x + 17 is x = − 2 . After isolating the variable and simplifying, we confirmed this answer through substitution. Thus, we can confidently say that the values are consistent and the solution is validated.
;
