Which Is The Solution To The Inequality?$\[ Y + 15 \ \textless \ 3 \\]A. \[$ Y \ \textless \ -12 \$\] B. \[$ Y \ \textgreater \ -12 \$\] C. \[$ Y \ \textless \ 18 \$\] D. \[$ Y \ \textgreater \ 18 \$\]

Introduction

In mathematics, inequalities are a fundamental concept that deals with the comparison of two or more values. A linear inequality is an inequality that involves a linear expression, which is an expression in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear inequalities, specifically the inequality $y + 15 < 3$. We will explore the different methods of solving linear inequalities and provide a step-by-step guide on how to solve them.

Understanding Linear Inequalities

A linear inequality is an inequality that involves a linear expression. It can be written in the form of $ax + b < c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. The inequality can be either greater than ($>$), less than ($<$), greater than or equal to ($\geq$), or less than or equal to ($\leq$).

Solving Linear Inequalities

To solve a linear inequality, we need to isolate the variable on one side of the inequality sign. We can do this by adding, subtracting, multiplying, or dividing both sides of the inequality by the same value.

Method 1: Adding or Subtracting

When we add or subtract a value from both sides of the inequality, the inequality sign remains the same.

Example 1

Solve the inequality $y + 15 < 3$.

y + 15 < 3
y + 15 - 15 < 3 - 15
y < -12

In this example, we added -15 to both sides of the inequality, which resulted in the solution $y < -12$.

Method 2: Multiplying or Dividing

When we multiply or divide both sides of the inequality by a value, we need to be careful not to change the direction of the inequality sign.

Example 2

Solve the inequality $y < 3$.

y < 3
y / 2 < 3 / 2
y / 2 < 1.5

In this example, we divided both sides of the inequality by 2, which resulted in the solution $y / 2 < 1.5$.

Method 3: Using Inverse Operations

When we use inverse operations to solve an inequality, we need to be careful not to change the direction of the inequality sign.

Example 3

Solve the inequality $y + 15 < 3$.

y + 15 < 3
y + 15 - 15 < 3 - 15
y < -12

In this example, we used the inverse operation of subtraction to solve the inequality, which resulted in the solution $y < -12$.

Conclusion

Solving linear inequalities is a crucial concept in mathematics that deals with the comparison of two or more values. By using the methods of adding or subtracting, multiplying or dividing, and using inverse operations, we can solve linear inequalities and find the solution. In this article, we solved the inequality $y + 15 < 3$ using the three methods and found the solution to be $y < -12$.

Which is the Solution to the Inequality?

Based on the solution we found in the previous section, the correct answer to the inequality $y + 15 < 3$ is:

• A. $y < -12$

This is the correct solution to the inequality, as we found in the previous section.

Final Answer

The final answer to the inequality $y + 15 < 3$ is:

• A. $y < -12$

This is the correct solution to the inequality, as we found in the previous section.