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solve the equation $az+17 = -4z-b$

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Solve linear equations

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Q. solve the equation

az+17 = -4z-b

Move $-4z$ to left: We have the equation $az + 17 = -4z - b$ . To start solving for $z$ , we need to get all the terms containing $z$ on one side of the equation. Let's move $-4z$ to the left side by adding $4z$ to both sides of the equation. $\newline$ $az + 17 + 4z = -4z - b + 4z$
Combine like terms: Now, let's combine like terms on both sides of the equation. $\newline$ $(az + 4z) + 17 = -b$ $\newline$ $a$ and $4$ are coefficients of $z$ , so we can add them together. $\newline$ $(a + 4)z + 17 = -b$
Isolate the term: Next, we need to isolate the term with $z$ . We can do this by subtracting $17$ from both sides of the equation. $(a + 4)z + 17 - 17 = -b - 17$ $(a + 4)z = -b - 17$
Divide by coefficient: Finally, to solve for $z$ , we need to divide both sides of the equation by the coefficient of $z$ , which is $(a + 4)$ . $\newline$ $z = \frac{-b - 17}{a + 4}$

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