Problem 34 - Elementary Algebra

Question

Solve each of the conditional equations. $$ y+6=-11 $$

Step-by-Step Solution

Answer

Answer: The value of y in the equation is $y = -17$.

Step 1: Identify the equation

We are given the equation $$y + 6 = -11$$ and asked to solve for y.

Step 2: Subtract 6 from both sides

To find the value of y, we will subtract 6 from both sides of the equation, like this: $$ y + 6 - 6 = -11 - 6 $$

Step 3: Simplify and solve for y

The simplified equation now becomes $$y = -11 - 6$$, which results in $$y = -17$$. Therefore, the solution to the given equation is $$y = -17$$.

Key Concepts

Conditional Equations

In algebra, a conditional equation is an equation that is true only for certain values of the variable. This means that the equation "conditions" the variable to meet specific criteria for it to hold true. Consider the equation we worked on: \( y + 6 = -11 \). This equation only holds true when the variable \( y \) is equal to -17. Conditional equations are the opposite of identities, which are true for all possible values of the variable.When solving a conditional equation, your goal is to find the specific value(s) that satisfy the equation. Identifying the condition that makes the equation true is essential when working with these types of problems.

Step-by-step Algebra Solution

A step-by-step algebra solution involves breaking down the process of solving an equation into manageable actions. This technique helps learners understand each part of the problem-solving process and apply similar steps to other algebraic equations. Let's take another look at the steps used to solve the equation \( y + 6 = -11 \):- **Step 1**: Identify the equation. We begin by stating the equation \( y + 6 = -11 \) and recognizing the necessity to solve for \( y \).- **Step 2**: Subtract 6 from both sides. This removes the constant from one side, allowing \( y \) to stand alone: \( y + 6 - 6 = -11 - 6 \)- **Step 3**: Simplify to solve for \( y \). After performing the operation, we find the value of \( y = -17 \).By following this systematic approach, students are better equipped to solve similar algebraic equations confidently and accurately.

Equation Simplification

Equation simplification is all about making an equation easier to solve. It involves performing operations to both sides of the equation to isolate the variable. The aim is to ultimately transform the equation into its simplest form, where it becomes more apparent what the solution will be.In our exercise:- We started with the equation \( y + 6 = -11 \).- By subtracting 6 from both sides, \( y + 6 - 6 = -11 - 6 \), we simplified it to \( y = -17 \).Simplifying an equation such as the one above doesn't change the solution—it just makes it clearer. Remember, whatever operation is done to one side of an equation must be done to the other side to maintain its balance.

Basic Algebra Problems

Basic algebra problems are one of the first steps in developing strong math skills. They typically involve finding an unknown variable using simple arithmetic operations such as addition, subtraction, multiplication, and division.The equation \( y + 6 = -11 \) is an example of a basic algebra problem. It tests your ability to:

• Understand the structure of an equation
• Manipulate the equation to isolate the unknown variable
• Solve the equation by applying arithmetic operations

Mastering basic algebra problems is crucial. They build the fundamental skills needed for more advanced topics in mathematics, allowing students to tackle more complex equations and systems in the future.