Solving 2x - 3 > 11 - 5x: Find the Value for X!
The solution set of 2x - 3 > 11 - 5x is the value of x that satisfies the inequality.
Have you ever wondered what value of x satisfies a given inequality? Well, look no further! In this case, we are interested in finding the solution set of the inequality 2x – 3 > 11 – 5x. By solving this inequality, we can determine the range of values that x can take in order for the inequality to hold true. So, let's dive into the world of inequalities and discover the value of x that makes this inequality valid!
Introduction
In order to find the value of x that is in the solution set of the inequality 2x – 3 > 11 – 5x, we need to solve the inequality by isolating x on one side of the equation. This article will guide you through the steps required to determine the value of x that satisfies the given inequality.
Step 1: Simplify the inequality
The first step is to simplify the inequality by combining like terms. We can do this by adding 5x to both sides of the equation and adding 3 to both sides as well. This will eliminate the negative sign and allow us to isolate x.
Step 2: Combine like terms
By adding 5x to both sides, we get: 7x - 3 > 11.
Step 3: Isolate x
Next, we want to isolate x on one side of the inequality. To do this, we add 3 to both sides of the equation. This gives us: 7x > 14.
Step 4: Divide by the coefficient of x
To solve for x, we need to divide both sides of the equation by the coefficient of x, which is 7. This will give us the value of x that satisfies the inequality. Dividing both sides by 7, we get: x > 2.
Step 5: Interpretation
The solution to the inequality 2x – 3 > 11 – 5x is x > 2. This means that any value of x greater than 2 will make the inequality true. In other words, if we substitute any number greater than 2 for x, the left side of the inequality will be greater than the right side.
Conclusion
In conclusion, to find the value of x that is in the solution set of the inequality 2x – 3 > 11 – 5x, we followed a systematic process of simplifying, combining like terms, isolating x, and dividing by the coefficient of x. By applying these steps, we determined that x > 2 is the solution to the given inequality. It is important to remember to always perform the same operations on both sides of the inequality to maintain its balance.
Note:
This article assumes basic knowledge of algebraic operations and solving inequalities. It is always recommended to double-check your work and verify the solution by substituting the value of x back into the original inequality to ensure its validity.
Introduction to the Inequality: Understanding the Problem Statement
Inequalities are mathematical expressions that compare two quantities and indicate their relationship using symbols such as greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤). In this problem, we are given the inequality 2x – 3 > 11 – 5x. Our goal is to determine the value(s) of x that satisfy this inequality, which means finding the solution set.
Simplifying the Inequality: Bringing Like Terms Together
To simplify the given inequality, we start by combining like terms on both sides of the equation. On the left side, we have 2x, and on the right side, we have -5x. We can rearrange the equation to bring all the x terms to one side.
Combining Like Terms on the Left Side: Rearranging the Equation
By adding 5x to both sides of the equation, we can eliminate the -5x term from the right side. This gives us 2x + 5x – 3 > 11.
Combining Like Terms on the Right Side: Simplifying the Equation Further
Next, we simplify the right side of the equation by combining the constants. We add 3 to both sides, resulting in 2x + 5x > 14.
Moving Variables to One Side: Establishing the Isolation of X
To isolate x as a single variable, we need to move the 5x term to the left side of the equation. By subtracting 5x from both sides, we get 2x > 14 - 5x.
Collecting Variables on the Left Side: Isolating X as a Single Variable
Now, we collect all the x terms on the left side of the equation. By adding 5x to both sides, we obtain 2x + 5x > 14.
Adjusting the Equation: Rearranging Terms to Add the Variables
We rearrange the equation by combining the x terms on the left side. This gives us 7x > 14.
Final Simplification: Bringing the Equation to its Simplest Form
To simplify further, we can divide both sides of the equation by 7. This results in x > 2.
Identifying the Solution Set: Determining the Values of X That Satisfy the Inequality
The solution set represents the values of x that satisfy the inequality. In this case, any value of x greater than 2 will satisfy the inequality 2x – 3 > 11 – 5x. Therefore, the solution set is x > 2.
Conclusion: Finalizing the Solution Set and Overall Understanding of the Problem
In conclusion, we have successfully solved the inequality 2x – 3 > 11 – 5x by simplifying and rearranging the equation. The solution set x > 2 indicates that any value of x greater than 2 will satisfy the inequality. This understanding allows us to confidently determine the range of values for x that make the inequality true.
In order to find the value of x that is in the solution set of the inequality 2x – 3 > 11 – 5x, we can follow these steps:
- Start by simplifying the inequality by combining like terms on both sides. We can do this by adding 5x to both sides and adding 3 to both sides. This gives us: 7x > 14.
- Next, divide both sides of the inequality by 7 in order to isolate x. This yields: x > 2.
Therefore, the value of x that is in the solution set of the inequality 2x – 3 > 11 – 5x is any number greater than 2. This means that x can take on values such as 3, 4, 5, and so on.
Thank you for visiting our blog and taking the time to read our article on finding the value of x in the solution set of 2x – 3 > 11 – 5x. We hope that this explanation has provided you with a clear understanding of how to solve this type of inequality and determine the possible values of x.
To find the solution set of the given inequality, we first need to simplify it by combining like terms. By adding 5x to both sides of the inequality and adding 3 to both sides, we get 7x > 14. Next, we divide both sides of the inequality by 7 to isolate x, resulting in x > 2. Therefore, any value of x greater than 2 will satisfy the original inequality.
It is important to note that the solution set of an inequality can be represented using interval notation or inequality notation. In this case, we would express the solution set as x > 2, indicating that x is greater than 2. This means that any value of x that is larger than 2, such as 3, 4, 5, and so on, would make the original inequality true.
We hope that this explanation has been helpful in clarifying how to find the value of x in the solution set of 2x – 3 > 11 – 5x. If you have any further questions or would like more information on this topic, please feel free to reach out to us. Thank you again for visiting our blog, and we hope to see you back soon for more informative articles!
What Value Of X Is In The Solution Set Of 2x – 3 > 11 – 5x?
People Also Ask:
1. How do I solve the inequality 2x – 3 > 11 – 5x?
To solve the inequality, we need to isolate the variable x on one side of the equation. First, let's simplify the equation by combining like terms:
2x + 5x > 11 + 3
7x > 14
Now, divide both sides of the inequality by 7 to solve for x:
x > 14/7
x > 2
Therefore, the solution set for the inequality 2x – 3 > 11 – 5x is x > 2.
2. Can x be equal to 2 in the given inequality?
No, x cannot be equal to 2 in the given inequality 2x – 3 > 11 – 5x. The inequality states that x must be greater than 2 (x > 2). If x were equal to 2, the inequality would not hold true. Therefore, 2 is not included in the solution set.
3. How can I represent the solution set of this inequality?
The solution set of the inequality 2x – 3 > 11 – 5x can be represented using interval notation or set notation. In interval notation, the solution set would be (2, ∞), indicating that x is greater than 2 and there is no upper bound. In set notation, the solution set can be expressed as {x | x > 2}.