Solve the equation.
$-9x + 1 = -x + 17$
Answer (1)
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.
Adding 9x to Both Sides First, let's add 9 x to both sides of the equation to get the x terms on the right side: − 9 x + 1 + 9 x = − x + 17 + 9 x 1 = 8 x + 17
Subtracting 17 from Both Sides Next, we subtract 17 from both sides to isolate the term with x :
1 − 17 = 8 x + 17 − 17 − 16 = 8 x
Dividing by 8 Finally, we divide both sides by 8 to solve for x :
8 − 16 = 8 8 x x = − 2
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 situations, such as calculating the cost of items, determining distances, and converting units. For example, if you know the cost of a taxi ride is a fixed fee plus a charge per mile, you can use a linear equation to determine the total cost based on the distance traveled. Similarly, if you are converting temperatures from Celsius to Fahrenheit, you use a linear equation.
