Solve The Inequality $6x + 9 \ \textgreater \ 57$.Which Of The Following Graphs Shows The Solution?

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Introduction

In this article, we will solve the inequality $6x + 9 \ \textgreater \ 57$ and determine which graph shows the solution. Inequalities are mathematical statements that compare two expressions and indicate whether one is greater than, less than, greater than or equal to, or less than or equal to the other. Solving an inequality involves finding the values of the variable that make the inequality true.

Understanding the Inequality

The given inequality is $6x + 9 \ \textgreater \ 57$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can do this by subtracting 9 from both sides of the inequality and then dividing both sides by 6.

Step 1: Subtract 9 from Both Sides

Subtracting 9 from both sides of the inequality gives us:

$$6x + 9 - 9 \ \textgreater \ 57 - 9$$

This simplifies to:

$$6x \ \textgreater \ 48$$

Step 2: Divide Both Sides by 6

Dividing both sides of the inequality by 6 gives us:

$$\frac{6x}{6} \ \textgreater \ \frac{48}{6}$$

This simplifies to:

$$x \ \textgreater \ 8$$

Graphing the Solution

To graph the solution, we need to find the values of $x$ that satisfy the inequality $x \ \textgreater \ 8$. This means that $x$ can be any value greater than 8.

Types of Graphs

There are several types of graphs that can be used to represent the solution to an inequality. The most common types of graphs are:

• Number Line Graph: This type of graph uses a number line to represent the values of $x$ that satisfy the inequality.
• Coordinate Plane Graph: This type of graph uses a coordinate plane to represent the values of $x$ and $y$ that satisfy the inequality.
• Interval Graph: This type of graph uses intervals to represent the values of $x$ that satisfy the inequality.

Which Graph Shows the Solution?

Based on the solution to the inequality $x \ \textgreater \ 8$, we can determine which graph shows the solution.

Number Line Graph

A number line graph is a graph that uses a number line to represent the values of $x$ that satisfy the inequality. In this case, the number line graph would show a line that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Coordinate Plane Graph

A coordinate plane graph is a graph that uses a coordinate plane to represent the values of $x$ and $y$ that satisfy the inequality. In this case, the coordinate plane graph would show a region that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Interval Graph

An interval graph is a graph that uses intervals to represent the values of $x$ that satisfy the inequality. In this case, the interval graph would show an interval that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Conclusion

In conclusion, the solution to the inequality $6x + 9 \ \textgreater \ 57$ is $x \ \textgreater \ 8$. This means that $x$ can be any value greater than 8. The graph that shows the solution is a number line graph, a coordinate plane graph, or an interval graph that extends to the right of 8.

Frequently Asked Questions

• What is the solution to the inequality $6x + 9 \ \textgreater \ 57$? The solution to the inequality $6x + 9 \ \textgreater \ 57$ is $x \ \textgreater \ 8$.
• Which graph shows the solution? The graph that shows the solution is a number line graph, a coordinate plane graph, or an interval graph that extends to the right of 8.
• How do I graph the solution? To graph the solution, you can use a number line graph, a coordinate plane graph, or an interval graph to represent the values of $x$ that satisfy the inequality.

Final Answer

The final answer is: $\boxed{x \ \textgreater \ 8}$

$$

Introduction

In this article, we will solve the inequality $6x + 9 \ \textgreater \ 57$ and determine which graph shows the solution. Inequalities are mathematical statements that compare two expressions and indicate whether one is greater than, less than, greater than or equal to, or less than or equal to the other. Solving an inequality involves finding the values of the variable that make the inequality true.

Understanding the Inequality

The given inequality is $6x + 9 \ \textgreater \ 57$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can do this by subtracting 9 from both sides of the inequality and then dividing both sides by 6.

Step 1: Subtract 9 from Both Sides

Subtracting 9 from both sides of the inequality gives us:

$$6x + 9 - 9 \ \textgreater \ 57 - 9$$

This simplifies to:

$$6x \ \textgreater \ 48$$

Step 2: Divide Both Sides by 6

Dividing both sides of the inequality by 6 gives us:

$$\frac{6x}{6} \ \textgreater \ \frac{48}{6}$$

This simplifies to:

$$x \ \textgreater \ 8$$

Graphing the Solution

To graph the solution, we need to find the values of $x$ that satisfy the inequality $x \ \textgreater \ 8$. This means that $x$ can be any value greater than 8.

Types of Graphs

There are several types of graphs that can be used to represent the solution to an inequality. The most common types of graphs are:

• Number Line Graph: This type of graph uses a number line to represent the values of $x$ that satisfy the inequality.
• Coordinate Plane Graph: This type of graph uses a coordinate plane to represent the values of $x$ and $y$ that satisfy the inequality.
• Interval Graph: This type of graph uses intervals to represent the values of $x$ that satisfy the inequality.

Which Graph Shows the Solution?

Based on the solution to the inequality $x \ \textgreater \ 8$, we can determine which graph shows the solution.

Number Line Graph

A number line graph is a graph that uses a number line to represent the values of $x$ that satisfy the inequality. In this case, the number line graph would show a line that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Coordinate Plane Graph

A coordinate plane graph is a graph that uses a coordinate plane to represent the values of $x$ and $y$ that satisfy the inequality. In this case, the coordinate plane graph would show a region that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Interval Graph

An interval graph is a graph that uses intervals to represent the values of $x$ that satisfy the inequality. In this case, the interval graph would show an interval that extends to the right of 8, indicating that $x$ can be any value greater than 8.

Conclusion

In conclusion, the solution to the inequality $6x + 9 \ \textgreater \ 57$ is $x \ \textgreater \ 8$. This means that $x$ can be any value greater than 8. The graph that shows the solution is a number line graph, a coordinate plane graph, or an interval graph that extends to the right of 8.

Frequently Asked Questions

Q: What is the solution to the inequality $6x + 9 \ \textgreater \ 57$?

A: The solution to the inequality $6x + 9 \ \textgreater \ 57$ is $x \ \textgreater \ 8$.

Q: Which graph shows the solution?

A: The graph that shows the solution is a number line graph, a coordinate plane graph, or an interval graph that extends to the right of 8.

Q: How do I graph the solution?

A: To graph the solution, you can use a number line graph, a coordinate plane graph, or an interval graph to represent the values of $x$ that satisfy the inequality.

Q: What is the meaning of the inequality $x \ \textgreater \ 8$?

A: The inequality $x \ \textgreater \ 8$ means that $x$ can be any value greater than 8.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding or subtracting the same value to both sides of the inequality and then dividing both sides by the same value.

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

A: A number line graph is a graph that uses a number line to represent the values of $x$ that satisfy the inequality, while a coordinate plane graph is a graph that uses a coordinate plane to represent the values of $x$ and $y$ that satisfy the inequality.

Q: How do I determine which graph shows the solution?

A: To determine which graph shows the solution, you need to analyze the inequality and determine which type of graph is most suitable for representing the solution.

Final Answer

The final answer is: $\boxed{x \ \textgreater \ 8}$