Problem 119 Solve the equation for the varia... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 119

Solve the equation for the variable. $$-47=6 b+1$$

Short Answer

Expert verified

b = -8

Step by step solution

- Subtract 1 from both sides

To isolate the term with the variable, subtract 1 from both sides of the equation: -47 - 1 = 6b + 1 - 1 This simplifies to: -48 = 6b

- Divide both sides by 6

Next, divide both sides of the equation by 6 to solve for the variable b: -48 / 6 = 6b / 6 This simplifies to: -8 = b

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Key Concepts

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

Isolating the Variable

The first key step to solving an equation like $ -47 = 6b + 1 $ is isolating the variable. Isolating the variable means getting the variable by itself on one side of the equation. This helps us solve for the unknown.

To do this, we need to move all other terms to the opposite side of the equation.

In our example equation, we have $ 6b $ plus 1 on the right side. To isolate $ 6b $, we need to remove the 1. We do this by subtracting 1 from both sides: $-47 - 1 = 6b + 1 - 1 $.

Simplifying it, we get $-48 = 6b $. Now, the term with the variable is isolated.

Inverse Operations

Inverse operations are operations that undo each other. Understanding these is crucial for solving equations.

For instance:

Addition is the inverse of subtraction
Multiplication is the inverse of division

In our given equation $ -47 = 6b + 1 $, we used subtraction as an inverse operation to cancel out the +1. After simplifying to $ -48 = 6b $, we then used division to isolate $ b $.

By dividing both sides by 6, we get: $-48/6 = 6b/6 $, which simplifies to $-8 = b $.

Algebraic Manipulation

Algebraic manipulation involves using various algebra rules to rearrange and solve equations. This is an essential skill in algebra.

Let's review our problem step-by-step:

Start with $ -47 = 6b + 1 $
Subtract 1 from both sides: $-47 - 1 = 6b + 1 - 1 $
This results in: $-48 = 6b $
Then, divide both sides by 6: $-48 / 6 = 6b / 6 $
Simplifying, we find: $ -8 = b $

By following these steps and understanding the rules, you can manipulate and solve any algebraic equation. Practice these techniques to master algebra.

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91影视

Solve the equation for the variable. $$-47=6 b+1$$

Short Answer

Step by step solution

- Subtract 1 from both sides

- Divide both sides by 6

Key Concepts

Isolating the Variable

Inverse Operations

Algebraic Manipulation

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