Select The Correct Answer.Which Equation Is True For The Value B = 10 B=10 B = 10 ?A. 2 ( B + 4 ) = 16 2(b+4)=16 2 ( B + 4 ) = 16 B. 2 ( B + 2 ) = 40 2(b+2)=40 2 ( B + 2 ) = 40 C. 3 ( B − 2 ) = 24 3(b-2)=24 3 ( B − 2 ) = 24 D. 2 ( 8 + B ) = 42 2(8+b)=42 2 ( 8 + B ) = 42 E. 3 ( B − 4 ) = 20 3(b-4)=20 3 ( B − 4 ) = 20

In mathematics, equations are used to represent relationships between variables. When we are given a value for one of the variables, we can substitute that value into the equation to find the solution. In this article, we will explore how to select the correct answer from a set of equations when we are given a value for one of the variables.

Understanding the Problem

We are given a value for the variable $b$, which is $b=10$. We need to select the correct equation from the options provided, which are:

A. $2(b+4)=16$ B. $2(b+2)=40$ C. $3(b-2)=24$ D. $2(8+b)=42$ E. $3(b-4)=20$

Substituting the Value into Each Equation

To determine which equation is true, we need to substitute the value of $b$ into each equation and solve for the variable.

Option A: $2(b+4)=16$

Substituting $b=10$ into the equation, we get:

$2(10+4)=16$

Expanding the equation, we get:

$2(14)=16$

Simplifying the equation, we get:

$28=16$

This equation is not true, as $28$ is not equal to $16$.

Option B: $2(b+2)=40$

Substituting $b=10$ into the equation, we get:

$2(10+2)=40$

Expanding the equation, we get:

$2(12)=40$

Simplifying the equation, we get:

$24=40$

This equation is not true, as $24$ is not equal to $40$.

Option C: $3(b-2)=24$

Substituting $b=10$ into the equation, we get:

$3(10-2)=24$

Expanding the equation, we get:

$3(8)=24$

Simplifying the equation, we get:

$24=24$

This equation is true, as $24$ is equal to $24$.

Option D: $2(8+b)=42$

Substituting $b=10$ into the equation, we get:

$2(8+10)=42$

Expanding the equation, we get:

$2(18)=42$

Simplifying the equation, we get:

$36=42$

This equation is not true, as $36$ is not equal to $42$.

Option E: $3(b-4)=20$

Substituting $b=10$ into the equation, we get:

$3(10-4)=20$

Expanding the equation, we get:

$3(6)=20$

Simplifying the equation, we get:

$18=20$

This equation is not true, as $18$ is not equal to $20$.

Conclusion

Based on the calculations above, we can see that only one equation is true when $b=10$. The correct answer is:

C. $3(b-2)=24$

This equation is true because when we substitute $b=10$ into the equation, we get $3(8)=24$, which is a true statement.

Tips for Solving Equations

When solving equations with a given value, it's essential to follow these tips:

• Substitute the value into each equation carefully.
• Expand and simplify the equation to check if it's true.
• Check if the equation is true by comparing the left-hand side and right-hand side of the equation.
• If the equation is not true, eliminate it as an option.

By following these tips, you can select the correct answer from a set of equations when you are given a value for one of the variables.

Common Mistakes to Avoid

When solving equations with a given value, it's essential to avoid these common mistakes:

• Not substituting the value into each equation carefully.
• Not expanding and simplifying the equation.
• Not checking if the equation is true.
• Not eliminating equations that are not true.

By avoiding these mistakes, you can ensure that you select the correct answer from a set of equations when you are given a value for one of the variables.

Real-World Applications

Solving equations with a given value has many real-world applications, such as:

• Calculating the cost of goods sold.
• Determining the profit or loss of a business.
• Finding the area or perimeter of a shape.
• Solving problems in physics, engineering, and other fields.

By understanding how to solve equations with a given value, you can apply this knowledge to real-world problems and make informed decisions.

Conclusion

In this article, we will answer some of the most frequently asked questions about solving equations with a given value.

Q: What is the first step in solving an equation with a given value?

A: The first step in solving an equation with a given value is to substitute the value into the equation. This means replacing the variable with the given value.

Q: How do I know if an equation is true or false?

A: To determine if an equation is true or false, you need to substitute the value into the equation and simplify it. If the left-hand side and right-hand side of the equation are equal, then the equation is true. If they are not equal, then the equation is false.

Q: What is the difference between a true equation and a false equation?

A: A true equation is one where the left-hand side and right-hand side of the equation are equal. A false equation is one where the left-hand side and right-hand side of the equation are not equal.

Q: How do I eliminate an equation that is not true?

A: To eliminate an equation that is not true, you need to substitute the value into the equation and simplify it. If the equation is not true, then you can eliminate it as an option.

Q: What is the importance of simplifying an equation?

A: Simplifying an equation is important because it helps you to determine if the equation is true or false. By simplifying the equation, you can compare the left-hand side and right-hand side of the equation and determine if they are equal.

Q: Can I use a calculator to solve an equation with a given value?

A: Yes, you can use a calculator to solve an equation with a given value. However, it's always a good idea to check your work by hand to make sure that the equation is true.

Q: How do I know if I have made a mistake when solving an equation with a given value?

A: To determine if you have made a mistake when solving an equation with a given value, you need to check your work carefully. Make sure that you have substituted the value into the equation correctly and that you have simplified the equation correctly.

Q: What should I do if I get stuck when solving an equation with a given value?

A: If you get stuck when solving an equation with a given value, don't be afraid to ask for help. You can ask a teacher, tutor, or classmate for assistance. You can also try re-reading the problem and breaking it down into smaller steps.

Q: How can I practice solving equations with a given value?

A: You can practice solving equations with a given value by working on problems in a textbook or online resource. You can also try creating your own problems and solving them.

Q: What are some common mistakes to avoid when solving equations with a given value?

A: Some common mistakes to avoid when solving equations with a given value include:

• Not substituting the value into the equation correctly
• Not simplifying the equation correctly
• Not checking if the equation is true
• Not eliminating equations that are not true

Q: How can I apply the skills I learn when solving equations with a given value to real-world problems?

A: You can apply the skills you learn when solving equations with a given value to real-world problems by using them to solve problems in physics, engineering, and other fields. You can also use them to calculate the cost of goods sold, determine the profit or loss of a business, and find the area or perimeter of a shape.

Conclusion

In conclusion, solving equations with a given value is an essential skill in mathematics. By following the tips and avoiding common mistakes, you can select the correct answer from a set of equations when you are given a value for one of the variables. Remember to substitute the value into each equation carefully, expand and simplify the equation, and check if the equation is true. With practice and patience, you can become proficient in solving equations with a given value and apply this knowledge to real-world problems.