Which Graph Represents The Solution Set For The Inequality $\frac{1}{2} X \leq 18$?

Introduction

In mathematics, inequalities are used to describe relationships between variables. They are essential in solving problems and making decisions in various fields, including science, engineering, economics, and finance. One of the most common types of inequalities is the linear inequality, which is an inequality involving a linear expression. In this article, we will focus on solving the linear inequality $\frac{1}{2} x \leq 18$ and determining which graph represents the solution set.

Understanding the Inequality

The given inequality is $\frac{1}{2} x \leq 18$. To solve this inequality, we need to isolate the variable $x$. We can start by multiplying both sides of the inequality by 2, which is the reciprocal of $\frac{1}{2}$. This will eliminate the fraction and make it easier to solve.

\frac{1}{2} x \leq 18
2 \times \frac{1}{2} x \leq 2 \times 18
x \leq 36

Graphing the Solution Set

Now that we have solved the inequality, we need to determine which graph represents the solution set. The solution set is the set of all values of $x$ that satisfy the inequality. In this case, the solution set is $x \leq 36$. To graph the solution set, we can use a number line or a coordinate plane.

Using a Number Line

A number line is a line that extends infinitely in both directions, with numbers marked at equal intervals. We can use a number line to graph the solution set by marking the point $x = 36$ and shading the region to the left of this point.

  -∞-------------------36-------------------∞
  |                         |
  |  x ≤ 36                |
  |                         |
  |________________________|

Using a Coordinate Plane

A coordinate plane is a two-dimensional plane with a horizontal axis (x-axis) and a vertical axis (y-axis). We can use a coordinate plane to graph the solution set by marking the point (36, 0) and shading the region below this point.

  +-------------------36-------------------+
  |                         |
  |  x ≤ 36                |
  |                         |
  |________________________|

Conclusion

In conclusion, the graph that represents the solution set for the inequality $\frac{1}{2} x \leq 18$ is the number line or coordinate plane with the point $x = 36$ marked and the region to the left or below this point shaded. This graph represents all values of $x$ that satisfy the inequality, which is $x \leq 36$.

Frequently Asked Questions

• What is the solution set for the inequality $\frac{1}{2} x \leq 18$?
• How do I graph the solution set for a linear inequality?
• What is the difference between a number line and a coordinate plane?

Final Answer

The final answer is the graph that represents the solution set for the inequality $\frac{1}{2} x \leq 18$, which is the number line or coordinate plane with the point $x = 36$ marked and the region to the left or below this point shaded.

Introduction

Linear inequalities are a fundamental concept in mathematics, and they have numerous applications in various fields, including science, engineering, economics, and finance. In our previous article, we discussed how to solve the linear inequality $\frac{1}{2} x \leq 18$ and determine which graph represents the solution set. In this article, we will answer some frequently asked questions (FAQs) about linear inequalities.

Q&A

Q1: What is a linear inequality?

A linear inequality is an inequality involving a linear expression. It is a mathematical statement that compares two expressions, where one expression is greater than, less than, or equal to the other expression.

Q2: How do I solve a linear inequality?

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

Q3: What is the difference between a linear inequality and a linear equation?

A linear equation is an equation involving a linear expression, where the variable is equal to the other expression. A linear inequality, on the other hand, is an inequality involving a linear expression, where the variable is not equal to the other expression.

Q4: How do I graph the solution set for a linear inequality?

To graph the solution set for a linear inequality, you need to mark the point that represents the solution to the inequality and shade the region that satisfies the inequality.

Q5: What is the solution set for a linear inequality?

The solution set for a linear inequality is the set of all values of the variable that satisfy the inequality.

Q6: How do I determine which graph represents the solution set for a linear inequality?

To determine which graph represents the solution set for a linear inequality, you need to identify the point that represents the solution to the inequality and the region that satisfies the inequality.

Q7: Can I use a number line or a coordinate plane to graph the solution set for a linear inequality?

Yes, you can use either a number line or a coordinate plane to graph the solution set for a linear inequality.

Q8: What is the difference between a number line and a coordinate plane?

A number line is a line that extends infinitely in both directions, with numbers marked at equal intervals. A coordinate plane, on the other hand, is a two-dimensional plane with a horizontal axis (x-axis) and a vertical axis (y-axis).

Q9: How do I use a number line to graph the solution set for a linear inequality?

To use a number line to graph the solution set for a linear inequality, you need to mark the point that represents the solution to the inequality and shade the region to the left or right of this point.

Q10: How do I use a coordinate plane to graph the solution set for a linear inequality?

To use a coordinate plane to graph the solution set for a linear inequality, you need to mark the point that represents the solution to the inequality and shade the region below or above this point.

Conclusion

In conclusion, linear inequalities are a fundamental concept in mathematics, and they have numerous applications in various fields. By understanding how to solve and graph linear inequalities, you can make informed decisions and solve problems in a variety of contexts.

Final Answer

The final answer is that linear inequalities are a fundamental concept in mathematics, and they have numerous applications in various fields. By understanding how to solve and graph linear inequalities, you can make informed decisions and solve problems in a variety of contexts.

Additional Resources

• Linear Inequalities Tutorial
• Graphing Linear Inequalities
• Linear Inequalities Practice Problems