az + 17 = -4z – b What is z?
The correct answer and explanation is:
We are given the equation: az+17=−4z−baz + 17 = -4z – b
Our goal is to solve for zz in terms of aa and bb.
Step 1: Move all terms involving zz to one side
az+4z+17=−baz + 4z + 17 = -b
This combines the zz-terms: z(a+4)+17=−bz(a + 4) + 17 = -b
Step 2: Isolate the zz-term
z(a+4)=−b−17z(a + 4) = -b – 17
Step 3: Solve for zz
Now divide both sides by (a+4)(a + 4), assuming a≠−4a \neq -4: z=−b−17a+4z = \frac{-b – 17}{a + 4}
✅ Final Answer:
z=−b−17a+4\boxed{z = \frac{-b – 17}{a + 4}}
📘 300-Word Explanation:
To solve the equation az+17=−4z−baz + 17 = -4z – b, the goal is to isolate the variable zz. The equation contains terms involving zz on both sides, as well as constants. The first step in solving such equations is to get all terms containing the variable zz on one side of the equation and constants on the other.
We begin by adding 4z4z to both sides. This helps eliminate the zz-term on the right-hand side: az+4z+17=−baz + 4z + 17 = -b
We then combine the like terms involving zz to simplify: z(a+4)+17=−bz(a + 4) + 17 = -b
Next, we subtract 17 from both sides to move the constant to the right: z(a+4)=−b−17z(a + 4) = -b – 17
Finally, to isolate zz, we divide both sides of the equation by a+4a + 4, which assumes that a+4≠0a + 4 \neq 0 (because division by zero is undefined): z=−b−17a+4z = \frac{-b – 17}{a + 4}
This is the simplest form of the expression that gives the value of zz in terms of aa and bb. It’s important to check that the denominator is not zero, otherwise the solution would not be valid.