Solve for $x$. $z=8 x-y$
Answer (2)
Add y to both sides of the equation: z + y = 8 x .
Divide both sides by 8: 8 z + y = x .
Simplify to find the solution for x .
The solution is: x = 8 z + y
Explanation
Understanding the Problem We are given the equation z = 8 x − y and we want to solve for x . This means we want to isolate x on one side of the equation.
Adding y to Both Sides To isolate x , we first need to get rid of the − y term on the right side of the equation. We can do this by adding y to both sides of the equation:
z + y = 8 x − y + y
This simplifies to:
z + y = 8 x
Dividing by 8 Now, we need to get rid of the 8 that is multiplying x . We can do this by dividing both sides of the equation by 8 :
8 z + y = 8 8 x
This simplifies to:
8 z + y = x
Final Answer Therefore, we have solved for x :
x = 8 z + y
Examples
In physics, this type of equation can represent a relationship between variables in a system. For example, if z represents the final position of an object, x represents its initial position, and y represents a displacement, the equation z = 8 x − y can model how these quantities are related. Solving for x allows you to determine the initial position given the final position and displacement. Understanding how to manipulate such equations is crucial for predicting and analyzing physical phenomena.
To solve for x in the equation z = 8 x − y , first add y to both sides to get z + y = 8 x , then divide by 8 to isolate x , resulting in x = 8 z + y .
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