Solve $4 z-5 y=w+4$ for $z$
Answer (1)
Add 5 y to both sides of the equation: 4 z = w + 4 + 5 y .
Divide both sides by 4 to isolate z : z = 4 w + 4 + 5 y .
Simplify the expression: z = 4 w + 5 y + 4 .
The solution for z is: z = 4 w + 5 y + 4
Explanation
Understanding the Problem We are given the equation 4 z − 5 y = w + 4 and asked to solve for z . This means we want to isolate z on one side of the equation and express it in terms of the other variables, w and y .
Isolating the z term To isolate z , we first add 5 y to both sides of the equation: 4 z − 5 y + 5 y = w + 4 + 5 y
4 z = w + 5 y + 4
Solving for z Now, we divide both sides of the equation by 4 to solve for z : 4 4 z = 4 w + 5 y + 4
z = 4 w + 5 y + 4
Final Answer Therefore, the solution for z in terms of w and y is: z = 4 w + 5 y + 4
Examples
Imagine you are baking a cake and need to adjust the recipe based on the ingredients you have. If the amount of flour ( z ) depends on the amount of sugar ( y ) and a special ingredient ( w ), this equation helps you calculate exactly how much flour you need. By rearranging the formula, you can easily find the required amount of flour for any combination of sugar and the special ingredient, ensuring your cake turns out perfectly every time.
