Question

Solve for z. Assume the equation has a solution for z, -p.(d+z) = -2z+59​

Answer 1

Answer:

$z = \boxed{ \frac{59 + pd}{2 - p} }$

General Formulas and Concepts:
Pre-Algebra

Distributive Property

Algebra I

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Terms/Coefficients

• Expanding/Factoring

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle -p(d + z) = -2z + 59$

Step 2: Solve for z

1. [Distributive Property] Distribute -p:
   $\displaystyle \begin{aligned}-p(d + z) = -2z + 59 & \rightarrow -pd -pz = -2z + 59 \\\end{aligned}$
2. [Addition Property of Equality] Add -2z to both sides:
   $\displaystyle \begin{aligned}-p(d + z) = -2z + 59 & \rightarrow -pd -pz = -2z + 59 \\& \rightarrow -pd -pz + 2z = 59 \\\end{aligned}$
3. [Addition Property of Equality] Add -pd to both sides:
   $\displaystyle \begin{aligned}-p(d + z) = -2z + 59 & \rightarrow -pd - pz = -2z + 59 \\& \rightarrow -pd - pz + 2z = 59 \\& \rightarrow -pz + 2z = 59 + pd \\\end{aligned}$
4. Factor:
   
   $\displaystyle \begin{aligned}-p(d + z) = -2z + 59 & \rightarrow -pd - pz = -2z + 59 \\& \rightarrow -pd - pz + 2z = 59 \\& \rightarrow -pz + 2z = 59 + pd \\& \rightarrow z(-p + 2) = 59 + pd \\\end{aligned}$
5. [Division Property of Equality] Divide -p + 2 on both sides:
   $\displaystyle \begin{aligned}-p(d + z) = -2z + 59 & \rightarrow -pd - pz = -2z + 59 \\& \rightarrow -pd - pz + 2z = 59 \\& \rightarrow -pz + 2z = 59 + pd \\& \rightarrow z(-p + 2) = 59 + pd \\& \rightarrow z = \boxed{ \frac{59 + pd}{2 - p} } \\\end{aligned}$

∴ we have solved the given equation for z.

___

Learn more about Algebra I: https://brainly.com/question/16452009

___

Topic: Algebra I