/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 \(-6(2 b+1)+(13 b-7)=0\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 87

\(-6(2 b+1)+(13 b-7)=0\)

Short Answer

Expert verified
b = 13

Step by step solution

01

- Distribute the Constants

Apply the distributive property to the left side of the equation: \ \(-6(2b + 1) + (13b - 7) = 0\). \ Multiply \(-6\) by each term inside the parentheses: \ \(-6 \times 2b + (-6) \times 1 = -12b - 6\). \ The equation now looks like: \ \(-12b - 6 + 13b - 7 = 0\).
02

- Combine Like Terms

Combine the like terms on the left side of the equation: \ \ \(-12b + 13b - 6 - 7 = 0\). \ Simplify: \ \(b - 13 = 0\).
03

- Solve for the Variable

Isolate the variable \(b\) by adding \(13\) to both sides of the equation: \ \ \(b - 13 + 13 = 0 + 13\). \ Simplify: \ \(b = 13\).

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Key Concepts

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

Distributive Property
The distributive property is crucial in solving many algebraic equations. It allows you to multiply a single term by each term within parentheses. In this exercise, we start with the equation: o(2b + 1). We distribute the o across the terms and in the parentheses: -6 (2b + 1) -6 (2b + (-6) o-12b - 6). oo-distribute 13b - 7 o-applications of distributors
Combining Like Terms
After distributing, the next step is to combine like terms. These are terms that have the same variable raised to the same power. In our equation: -12b - 6 + 13b - 6= 0First, we combine the b-terms: -12b + 13b 1b bNext, we combine the constant terms: -6 -13 Thus, simplified equation:=b-13=0 this step are simple Can be'sequencing

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