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Chapter 8: Problem 337

In the following exercises, solve each equation. $$ -(d+9)=23 $$

Short Answer

Expert verified
d = -32

Step by step solution

01

Distribute the negative sign

First, distribute the negative sign inside the parentheses to get -(d+9) = 23 i.e., -d - 9 = 23.
02

Isolate the variable

Add 9 to both sides of the equation to start isolating the variable: -d - 9 + 9 = 23 + 9 This simplifies to: -d = 32.
03

Solve for the variable

Multiply both sides of the equation by -1 to solve for d: -1(-d) = 32(-1) This simplifies to: d = -32.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
In algebra, the distributive property is an essential rule. This property allows you to multiply a single term by each term inside parentheses. In the given problem, the equation is -(d+9) = 23. Here, we distribute the negative sign (or -1) by multiplying it with every term inside the parentheses: -d - 9 = 23. No complex operations are needed. The key is just to apply the negative sign to each term inside the parentheses.
Isolating the Variable
To solve linear equations, we often need to isolate the variable. This means getting the variable by itself on one side of the equation. For our problem, we have: -d - 9 = 23. The variable here is d. To isolate it, we start by adding 9 to both sides of the equation:-d - 9 + 9 = 23 + 9. This simplifies to: -d = 32. Adding the same number to both sides keeps the equation balanced and moves us closer to finding our variable.
Basic Algebraic Operations
Basic algebraic operations include adding, subtracting, multiplying, and dividing terms. These operations are important for isolating and solving for variables. In the final step of our problem, we have: -d = 32. To solve for d, we need to eliminate the negative sign. We do this by multiplying both sides of the equation by -1: -1(-d) = 32(-1). This simplifies to: d = -32. By performing basic operations step-by-step, we manage to solve for the variable efficiently.

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