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 is − 2 .
Explanation
Understanding the Problem We are given the equation − 9 x + 1 = − x + 17 and asked to solve for x . We will use algebraic manipulation to isolate x on one side of the equation.
Adding 9 x to both sides First, we want to get all the x terms on one side of the equation. Let's add 9 x to both sides of the equation: − 9 x + 1 + 9 x = − x + 17 + 9 x 1 = 8 x + 17
Subtracting 17 from both sides Next, we want to isolate the x term. Subtract 17 from both sides of the equation: 1 − 17 = 8 x + 17 − 17 − 16 = 8 x
Dividing both sides by 8 Finally, divide both sides by 8 to solve for x :
8 − 16 = 8 8 x − 2 = x
Checking the Solution Therefore, the solution to the equation is x = − 2 . We can check this solution by substituting x = − 2 back into the original equation: − 9 ( − 2 ) + 1 = − ( − 2 ) + 17 18 + 1 = 2 + 17 19 = 19 Since the equation holds true, our solution is correct.
Final Answer 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 with a fixed price and a variable quantity. For example, if a phone plan costs $10 per month plus $0.05 per text message, you can use a linear equation to determine the total cost for a given number of text messages. Similarly, in physics, linear equations can describe the motion of an object moving at a constant velocity.
