Substitute the value back into the equation

Oct 13, 2025 by wbrum.org 8 views

Introduction

Equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore the concept of equations and provide a step-by-step guide on how to solve them. We will also discuss the different types of equations and how to check the answer.

What is an Equation?

An equation is a mathematical statement that states that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS is the expression on the left side of the equation, and the RHS is the expression on the right side.

Types of Equations

There are several types of equations, including:

Linear equations: These are equations in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation.
Quadratic equations: These are equations in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.
Polynomial equations: These are equations in which the highest power of the variable is a positive integer. For example, x^3 + 2x^2 - 3x + 1 = 0 is a polynomial equation.

How to Solve Equations

Solving an equation involves finding the value of the variable that makes the equation true. Here are the steps to solve an equation:

Read the equation: Read the equation carefully and understand what it is asking for.
Identify the variable: Identify the variable in the equation and what it represents.
Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Solve for the variable: Solve for the variable by performing the necessary operations to isolate it.

Checking the Answer

Once you have solved an equation, it is essential to check the answer to ensure that it is correct. Here are some ways to check the answer:

Substitute the value back into the equation: Substitute the value of the variable back into the original equation to see if it is true.
Use a calculator: Use a calculator to check the answer.
Check the units: Check the units of the answer to ensure that they are correct.

Which of the Following Choices Can be Used to Check the Answer in this Equation?

Let's consider the equation 205 - 110 = 95. To check the answer, we can use the following choices:

A. 205 + 95 = 300 B. 110 + 95 = 205 C. 205 + 110 = 315 D. 205 + 110 + 95 = 410

To check the answer, we can substitute the value of the variable back into the original equation. Let's try choice A:

205 + 95 = 300

This is not equal to 95, so choice A is not correct.

Let's try choice B:

110 + 95 = 205

This is equal to 205, not 95, so choice B is not correct.

Let's try choice C:

205 + 110 = 315

This is not equal to 95, so choice C is not correct.

Let's try choice D:

205 + 110 + 95 = 410

This is not equal to 95, so choice D is not correct.

However, we can try a different approach. Let's add 110 to both sides of the equation:

205 - 110 = 95 205 = 95 + 110

Now, let's add 95 to both sides of the equation:

205 = 95 + 110 205 = 205

This shows that the original equation is true, and the answer is correct.

Conclusion

In conclusion, solving equations is a crucial skill for students to master. By following the steps outlined in this article, students can learn how to solve equations and check their answers. Remember to always read the equation carefully, identify the variable, isolate the variable, and solve for the variable. Finally, check the answer by substituting the value back into the original equation or using a calculator.

Frequently Asked Questions

Q: What is an equation?

A: An equation is a mathematical statement that states that two expressions are equal.

Q: What are the different types of equations?

A: There are several types of equations, including linear equations, quadratic equations, and polynomial equations.

Q: How do I solve an equation?

A: To solve an equation, follow these steps: read the equation, identify the variable, isolate the variable, and solve for the variable.

Q: How do I check the answer?

A: To check the answer, substitute the value of the variable back into the original equation or use a calculator.

Q: What is the correct choice to check the answer in the equation 205 - 110 = 95?

Q&A: Solving Equations

Q: What is an equation?

A: An equation is a mathematical statement that states that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS is the expression on the left side of the equation, and the RHS is the expression on the right side.

Q: What are the different types of equations?

A: There are several types of equations, including:

Linear equations: These are equations in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation.
Quadratic equations: These are equations in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.
Polynomial equations: These are equations in which the highest power of the variable is a positive integer. For example, x^3 + 2x^2 - 3x + 1 = 0 is a polynomial equation.

Q: How do I solve an equation?

A: To solve an equation, follow these steps:

Read the equation: Read the equation carefully and understand what it is asking for.
Identify the variable: Identify the variable in the equation and what it represents.
Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Solve for the variable: Solve for the variable by performing the necessary operations to isolate it.

Q: How do I check the answer?

A: To check the answer, substitute the value of the variable back into the original equation or use a calculator.

Q: What is the correct choice to check the answer in the equation 205 - 110 = 95?

A: The correct choice is not listed among the options. However, we can try a different approach by adding 110 to both sides of the equation and then adding 95 to both sides of the equation. This shows that the original equation is true, and the answer is correct.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include:

Not reading the equation carefully: Make sure to read the equation carefully and understand what it is asking for.
Not identifying the variable: Identify the variable in the equation and what it represents.
Not isolating the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Not checking the answer: Make sure to check the answer by substituting the value of the variable back into the original equation or using a calculator.

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

A: To determine if an equation is true or false, substitute the value of the variable back into the original equation or use a calculator. If the equation is true, the value of the variable will make the equation true. If the equation is false, the value of the variable will not make the equation true.

Q: Can I use a calculator to solve equations?

A: Yes, you can use a calculator to solve equations. However, make sure to check the answer by substituting the value of the variable back into the original equation or using a calculator.

Q: What are some real-world applications of solving equations?

A: Solving equations has many real-world applications, including:

Science: Solving equations is used to model real-world phenomena, such as the motion of objects and the behavior of populations.
Engineering: Solving equations is used to design and optimize systems, such as bridges and buildings.
Economics: Solving equations is used to model economic systems and make predictions about future economic trends.
Computer Science: Solving equations is used to develop algorithms and solve problems in computer science.

Conclusion

In conclusion, solving equations is a crucial skill for students to master. By following the steps outlined in this article, students can learn how to solve equations and check their answers. Remember to always read the equation carefully, identify the variable, isolate the variable, and solve for the variable. Finally, check the answer by substituting the value of the variable back into the original equation or using a calculator.