Solve for z. Assume the equation has a solution for z. {:[-p*(d+z)=-2z+59],[z=◻]:}

Identify the system: Identify the system of equations. We have the following system of equations: 1. -p*(d+z) = -2z + 59 2. z = ◻ (We need to find the value of z)Isolate z in the first equation: Isolate z in the first equation. To isolate z, we need to distribute the -p across (d+z) and then move all terms containing z to one side of the equation. -p*d - p*z = -2z + 59Combine like terms: Combine like terms. Add p*z to both sides of the equation to get all the z terms on one side. -p*d = -2z + p*z + 59Factor out z on the right side: Factor out z on the right side of the equation. -p*d = z*(-2 + p) + 59Isolate z by subtracting 59: Isolate z by subtracting 59 from both sides and then dividing by (-2 + p). -p*d - 59 = z*(-2 + p) z = (-p*d - 59) / (-2 + p)Check if the value of p is valid: Check if the value of p is such that the denominator is not zero. We must ensure that -2 + p ≠ 0, otherwise, we cannot divide by zero. Since we are not given a specific value for p, we assume that p ≠ 2, which is a condition for the solution to exist.

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Solve for
z.
Assume the equation has a solution for
z.

{:[-p*(d+z)=-2z+59],[z=◻]:}

Solve for $z$ . $\newline$ Assume the equation has a solution for $z$ . $\newline$ $\begin{array}{l} -p \cdot(d+z)=-2 z+59 \\ z=\square \end{array}$

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Math Problems

Algebra 1

Rearrange multi-variable equations

Full solution

Q. Solve for

z

\newline

Assume the equation has a solution for

z

\newline

\begin{array}{l} -p \cdot(d+z)=-2 z+59 \\ z=\square \end{array}

Identify the system: Identify the system of equations. $\newline$ We have the following system of equations: $\newline$ $1$ . $-p(d+z) = -2z + 59$ $\newline$ $2$ . $z = \square$ (We need to find the value of $z$ )
Isolate $z$ in the first equation: Isolate $z$ in the first equation. $\newline$ To isolate $z$ , we need to distribute the $-p$ across $(d+z)$ and then move all terms containing $z$ to one side of the equation. $\newline$ $-p \cdot d - p \cdot z =$ $-2$ z + $59$
Combine like terms: Combine like terms. $\newline$ Add $p imes z$ to both sides of the equation to get all the $z$ terms on one side. $\newline$ $-p imes d = -2z + p imes z + 59$
Factor out $z$ on the right side: Factor out $z$ on the right side of the equation.
$-p \cdot d = z \cdot (-2 + p) + 59$
Isolate $z$ by subtracting $59$ : Isolate $z$ by subtracting $59$ from both sides and then dividing by $(-2 + p)$ . $\newline$ $-p \cdot d - 59 = z \cdot (-2 + p)$ $\newline$ $z = \frac{-p \cdot d - 59}{-2 + p}$
Check if the value of $p$ is valid: Check if the value of $p$ is such that the denominator is not zero. $\newline$ We must ensure that $-2$ + p \neq $0$ , otherwise, we cannot divide by zero. Since we are not given a specific value for $p$ , we assume that $p \neq$ $2$ , which is a condition for the solution to exist.