Problem 22 Solve using the addition princip... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 22

Solve using the addition principle. $$ y-6=-12 $$

Short Answer

Expert verified

y = -6

Step by step solution

Identify the Equation

The given equation is \[ y - 6 = -12 \] We need to solve for $ y $.

Apply the Addition Principle

To isolate $ y $, add 6 to both sides of the equation to offset the -6 on the left side. This gives us \[ y - 6 + 6 = -12 + 6 \]

Simplify Both Sides

Simplify the equation by performing the operations on both sides. \[ y = -6 \]

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Key Concepts

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

Solving Equations

When we talk about solving equations in basic algebra, we mean finding the value of the variable that makes the equation true. An equation is a mathematical statement where two expressions are equal. For instance, in the exercise \[ y - 6 = -12 \], we need to determine the value of $ y $ that satisfies this equation. The process involves performing operations on both sides of the equation to maintain the equality while making the variable isolated on one side. This step-by-step problem-solving method helps us identify the variable's value clearly.

Isolate Variable

One of the core steps in solving equations is isolating the variable. This means making the variable stand alone on one side of the equation. In our example \[ y - 6 = -12 \], we need to get $ y $ by itself. To do this, we use the addition principle.

The addition principle lets us add or subtract the same number from both sides of the equation without changing its equality.
For our exercise, we added 6 to both sides: \[ y - 6 + 6 = -12 + 6 \]
By simplifying, we achieve \[ y = -6 \]

This means $ y $ is isolated, and we鈥檝e found its value.

Basic Algebra

In basic algebra, understanding how to manipulate and solve equations is fundamental. Here are some essential points:

Operations: Addition, subtraction, multiplication, and division rules must be applied uniformly to both sides of an equation to maintain balance.
Principles: Principles like the addition principle help in managing terms and isolating variables.
Simplicity: Keep equations as simple as possible at each step to avoid mistakes.

By mastering these concepts, students can solve increasingly complex problems. For our exercise, using these basics, we found that \[ y = -6 \]. This result stems from understanding how to balance and simplify equations effectively.

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91影视

Solve using the addition principle. $$ y-6=-12 $$

Short Answer

Step by step solution

Identify the Equation

Apply the Addition Principle

Simplify Both Sides

Key Concepts

Solving Equations

Isolate Variable

Basic Algebra

One App. One Place for Learning.

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