Solve The Following Inequality And Graph The Solution Set On A Number Line.$\[ -8x \geq -16 \\]What Is The Solution? \[$\{x \mid \ \square\}\$\] (Type An Inequality.)Choose The Correct Graph Below.A. B. C. D.
Introduction
Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to symbols. Solving and graphing inequalities is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we will focus on solving and graphing the inequality -8x ≥ -16 and provide a step-by-step guide on how to approach similar problems.
Understanding the Inequality
The given inequality is -8x ≥ -16. To solve this inequality, we need to isolate the variable x on one side of the inequality sign. The first step is to divide both sides of the inequality by -8. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign.
Step 1: Divide Both Sides by -8
To solve the inequality, we will divide both sides by -8. However, since we are dividing by a negative number, we need to reverse the direction of the inequality sign.
-8x / -8 ≥ -16 / -8
x ≤ 2
Step 2: Graph the Solution Set
Now that we have solved the inequality, we need to graph the solution set on a number line. The solution set is the set of all values of x that satisfy the inequality. In this case, the solution set is x ≤ 2.
To graph the solution set, we will use a number line and mark the point 2 with an open circle. This represents the endpoint of the solution set. Since the inequality is x ≤ 2, we will shade the region to the left of the point 2 to indicate that all values of x less than or equal to 2 are part of the solution set.
Graphing the Solution Set
Here is the graph of the solution set:
-∞
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<br/>
**Solving and Graphing Inequalities: A Q&A Article**
=====================================================
**Q: What is an inequality?**
--------------------------------
A: An inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to symbols.
**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, subtracting, multiplying, or dividing both sides of the inequality by the same value.
**Q: What is the difference between a linear inequality and a quadratic inequality?**
------------------------------------------------------------
A: A linear inequality is an inequality that can be written in the form `ax + b ≥ c` or `ax + b ≤ c`, where `a`, `b`, and `c` are constants. A quadratic inequality is an inequality that can be written in the form `ax^2 + bx + c ≥ 0` or `ax^2 + bx + c ≤ 0`, where `a`, `b`, and `c` are constants.
**Q: How do I graph an inequality on a number line?**
------------------------------------------------
A: To graph an inequality on a number line, you need to identify the solution set, which is the set of all values of `x` that satisfy the inequality. You can do this by marking the point that separates the solution set from the rest of the number line. If the inequality is of the form `x ≥ a`, you will shade the region to the right of the point `a`. If the inequality is of the form `x ≤ a`, you will shade the region to the left of the point `a`.
**Q: What is the solution set of an inequality?**
--------------------------------------------
A: The solution set of an inequality is the set of all values of `x` that satisfy the inequality. It is the set of all values that make the inequality true.
**Q: How do I determine the solution set of an inequality?**
---------------------------------------------------
A: To determine the solution set of an inequality, you need to isolate the variable on one side of the inequality sign and then identify the values of `x` that satisfy the inequality.
**Q: What is the difference between a strict inequality and a non-strict inequality?**
------------------------------------------------------------
A: A strict inequality is an inequality that is written with a strict inequality symbol, such as `<` or `>`. A non-strict inequality is an inequality that is written with a non-strict inequality symbol, such as `≤` or `≥`.
**Q: How do I solve a system of inequalities?**
--------------------------------------------
A: To solve a system of inequalities, you need to solve each inequality separately and then find the intersection of the solution sets.
**Q: What is the intersection of two sets?**
-----------------------------------------
A: The intersection of two sets is the set of all elements that are common to both sets.
**Q: How do I find the intersection of two sets?**
--------------------------------------------
A: To find the intersection of two sets, you need to identify the elements that are common to both sets and then list them.
**Q: What is the union of two sets?**
--------------------------------
A: The union of two sets is the set of all elements that are in either set.
**Q: How do I find the union of two sets?**
-----------------------------------------
A: To find the union of two sets, you need to list all the elements that are in either set.
**Q: What is the difference between a set and a subset?**
------------------------------------------------
A: A set is a collection of elements. A subset is a set that is contained within another set.
**Q: How do I determine if a set is a subset of another set?**
---------------------------------------------------
A: To determine if a set is a subset of another set, you need to check if all the elements of the set are also elements of the other set.
**Q: What is the difference between a set and a proper subset?**
------------------------------------------------
A: A set is a collection of elements. A proper subset is a set that is contained within another set and is not equal to the other set.
**Q: How do I determine if a set is a proper subset of another set?**
------------------------------------------------------------
A: To determine if a set is a proper subset of another set, you need to check if all the elements of the set are also elements of the other set and if the set is not equal to the other set.
**Q: What is the difference between a set and a proper superset?**
------------------------------------------------
A: A set is a collection of elements. A proper superset is a set that contains another set and is not equal to the other set.
**Q: How do I determine if a set is a proper superset of another set?**
------------------------------------------------------------
A: To determine if a set is a proper superset of another set, you need to check if the set contains all the elements of the other set and if the set is not equal to the other set.
**Q: What is the difference between a set and a proper subset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper subset of a set is a set that is contained within the set and is not equal to the set.
**Q: How do I determine if a set is a proper subset of a set?**
---------------------------------------------------
A: To determine if a set is a proper subset of a set, you need to check if all the elements of the set are also elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper superset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper superset of a set is a set that contains the set and is not equal to the set.
**Q: How do I determine if a set is a proper superset of a set?**
---------------------------------------------------
A: To determine if a set is a proper superset of a set, you need to check if the set contains all the elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper subset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper subset of a set is a set that is contained within the set and is not equal to the set.
**Q: How do I determine if a set is a proper subset of a set?**
---------------------------------------------------
A: To determine if a set is a proper subset of a set, you need to check if all the elements of the set are also elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper superset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper superset of a set is a set that contains the set and is not equal to the set.
**Q: How do I determine if a set is a proper superset of a set?**
---------------------------------------------------
A: To determine if a set is a proper superset of a set, you need to check if the set contains all the elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper subset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper subset of a set is a set that is contained within the set and is not equal to the set.
**Q: How do I determine if a set is a proper subset of a set?**
---------------------------------------------------
A: To determine if a set is a proper subset of a set, you need to check if all the elements of the set are also elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper superset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper superset of a set is a set that contains the set and is not equal to the set.
**Q: How do I determine if a set is a proper superset of a set?**
---------------------------------------------------
A: To determine if a set is a proper superset of a set, you need to check if the set contains all the elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper subset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper subset of a set is a set that is contained within the set and is not equal to the set.
**Q: How do I determine if a set is a proper subset of a set?**
---------------------------------------------------
A: To determine if a set is a proper subset of a set, you need to check if all the elements of the set are also elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper superset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper superset of a set is a set that contains the set and is not equal to the set.
**Q: How do I determine if a set is a proper superset of a set?**
---------------------------------------------------
A: To determine if a set is a proper superset of a set, you need to check if the set contains all the elements of the set and if the set is not equal to the set.
**Q: What is the difference between a set and a proper subset of a set?**
------------------------------------------------------------
A: A set is a collection of elements. A proper subset of a set is a set that