Problem 15 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 15

Solve using the addition principle. $$ y+9=-9 $$

Short Answer

Expert verified

y = -18

Step by step solution

Understand the Equation

We have the equation: $ y + 9 = -9 $. Our goal is to isolate the variable $ y $.

Apply the Addition Principle

To isolate $ y $, we need to eliminate the constant term on the left side. We do this by subtracting 9 from both sides of the equation. Subtract 9 from both sides: $ y + 9 - 9 = -9 - 9 $

Simplify Both Sides

After subtracting 9 from both sides, we simplify the equation: $ y = -18 $.

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Key Concepts

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

Solving Equations

When solving equations, our primary goal is to find the value of the variable that makes the equation true. Equations often have equal signs, indicating that two expressions are equal. To solve for variables, we need to 'balance' the equation. This means performing the same operation on both sides.
In the example provided, the equation is: $ y + 9 = -9 $. By solving it, we seek the unknown value of $ y $ which makes both sides equal. Always remember to keep the equation balanced by applying the same arithmetic operation on both sides.

Isolating Variables

Isolating the variable means getting the variable by itself on one side of the equation. This is crucial for finding its value.
To isolate $ y $ in the equation $ y + 9 = -9 $, we use the addition principle. Essentially, we need to eliminate the constant added to $ y $. To achieve this, we subtract 9 from both sides:
\ y + 9 - 9= -9 - 9 \
After subtraction, the equation simplifies to $ y = -18 $.
The addition principle helps keep the equation balanced while effectively isolating the variable.

Basic Algebra

Basic algebra deals with manipulating algebraic expressions and solving equations. Key concepts include understanding variables, constants, and arithmetic operations. In our exercise, we encountered a fundamental situation where we needed to isolate the variable using addition and subtraction.
Here are some vital points to remember:

Variables are symbols representing unknown values (like $ y $ in our example).
Constants are known values (like the number 9 in our equation).
Operations like addition and subtraction help manipulate these expressions to solve for variables.

By understanding these basics, we can skillfully approach and solve algebraic equations.

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91影视

Solve using the addition principle. $$ y+9=-9 $$

Short Answer

Step by step solution

Understand the Equation

Apply the Addition Principle

Simplify Both Sides

Key Concepts

Solving Equations

Isolating Variables

Basic Algebra

One App. One Place for Learning.

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