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Chapter 8: Problem 6

In the following exercises, solve each equation. $$ y+5=-6 $$

Short Answer

Expert verified
y = -11

Step by step solution

01

- Identify the Equation

Given the equation: y + 5 = -6
02

- Isolate the Variable

To isolate the variable y, subtract 5 from both sides of the equation:y + 5 - 5 = -6 - 5
03

- Simplify Both Sides

Simplify the left side and the right side of the equation:y = -11

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Key Concepts

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

Isolating Variables
To solve linear equations, one of the first steps is to isolate the variable. This means getting the variable you are solving for all by itself on one side of the equals sign. For example, in the equation $$ y + 5 = -6 $$, you need to isolate y. You do this by performing operations that will move all other numbers to the opposite side. Here, you subtract 5 from both sides to achieve isolation: $$ y + 5 - 5 = -6 - 5 $$. This results in $$ y = -11 $$. Isolating the variable is crucial because it directly leads you to the solution of the equation.
Simplifying Equations
Simplifying equations involves reducing them to their simplest form. Once you perform the necessary operations to isolate the variable, you need to simplify both sides. Simplification makes equations easier to understand and solve. When we subtracted 5 from both sides in our example, we simplified the right side of the equation: $$ -6 - 5 = -11 $$. The simplified form of the equation is now $$ y = -11 $$ without any extra terms or numbers. Simplification is essential for clarity and accuracy in solving equations.
Basic Algebra
Basic algebra is the foundation of solving equations. It involves understanding operations like addition, subtraction, multiplication, and division. Basic algebra also includes concepts like isolating variables and simplifying equations. In our given problem $$ y + 5 = -6 $$, you apply subtraction, a basic algebraic operation, to both sides. By consistently applying these fundamental operations and principles, you can solve even more complex equations. Mastering basic algebra equips you with the skills needed for higher-level math and problem-solving in various fields.

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