Understanding the Basics of Algebraic Equations

Oct 13, 2025 by leolavanderia.com.br 29 views

**Match Each Equation with the Problem it Represents: A Comprehensive Guide**

Understanding the Basics of Algebraic Equations

Algebraic equations are a fundamental concept in mathematics, and they play a crucial role in solving various problems in different fields. In this article, we will explore four algebraic equations and match each of them with the problem it represents.

Equation 1: 4 more than the product of 9 and a number is 36

Let's start by analyzing the first equation: 4 more than the product of 9 and a number is 36. This equation can be represented as:

9x + 4 = 36

To solve for x, we need to isolate the variable x. We can do this by subtracting 4 from both sides of the equation:

9x = 32

Next, we divide both sides of the equation by 9:

x = 32/9

x = 3.56 (approximately)

Now that we have the value of x, let's think about what this equation represents. The equation 9x + 4 = 36 tells us that 4 more than the product of 9 and a number is equal to 36. This means that if we multiply 9 by a number and add 4 to the result, we get 36.

Equation 2: 9 times the sum of a number and 4 is 36

The second equation is: 9 times the sum of a number and 4 is 36. This equation can be represented as:

9(x + 4) = 36

To solve for x, we need to isolate the variable x. We can do this by dividing both sides of the equation by 9:

x + 4 = 36/9

x + 4 = 4

Next, we subtract 4 from both sides of the equation:

x = 0

Now that we have the value of x, let's think about what this equation represents. The equation 9(x + 4) = 36 tells us that 9 times the sum of a number and 4 is equal to 36. This means that if we multiply 9 by the sum of a number and 4, we get 36.

Equation 3: 4 times the sum of a number and 9 is 36

The third equation is: 4 times the sum of a number and 9 is 36. This equation can be represented as:

4(x + 9) = 36

To solve for x, we need to isolate the variable x. We can do this by dividing both sides of the equation by 4:

x + 9 = 36/4

x + 9 = 9

Next, we subtract 9 from both sides of the equation:

x = 0

Now that we have the value of x, let's think about what this equation represents. The equation 4(x + 9) = 36 tells us that 4 times the sum of a number and 9 is equal to 36. This means that if we multiply 4 by the sum of a number and 9, we get 36.

Equation 4: 9 subtracted from the product of 4 and a number is 36

The fourth equation is: 9 subtracted from the product of 4 and a number is 36. This equation can be represented as:

4x - 9 = 36

To solve for x, we need to isolate the variable x. We can do this by adding 9 to both sides of the equation:

4x = 45

Next, we divide both sides of the equation by 4:

x = 45/4

x = 11.25

Now that we have the value of x, let's think about what this equation represents. The equation 4x - 9 = 36 tells us that 9 subtracted from the product of 4 and a number is equal to 36. This means that if we multiply 4 by a number and subtract 9 from the result, we get 36.

Conclusion

In this article, we have explored four algebraic equations and matched each of them with the problem it represents. We have seen that each equation represents a different problem, and we have solved for the variable x in each equation. By understanding the basics of algebraic equations, we can solve a wide range of problems in mathematics and other fields.

Frequently Asked Questions

Q: What is an algebraic equation? A: An algebraic equation is a mathematical statement that contains a variable and an equal sign. It is used to represent a relationship between the variable and a constant.

Q: How do I solve an algebraic equation? A: To solve an algebraic equation, you need to isolate the variable by performing operations on both sides of the equation.

Q: What is the difference between an equation and an expression? A: An equation is a mathematical statement that contains an equal sign, while an expression is a mathematical statement that does not contain an equal sign.

Q: Can I use algebraic equations to solve real-world problems? A: Yes, algebraic equations can be used to solve a wide range of real-world problems, including problems in physics, engineering, economics, and more.

Q: How do I choose the correct equation to solve a problem? A: To choose the correct equation, you need to read the problem carefully and identify the key elements, such as the variable and the constant. Then, you can select the equation that best represents the problem.

Q: Can I use algebraic equations to solve problems with multiple variables? A: Yes, algebraic equations can be used to solve problems with multiple variables. However, you need to be careful to isolate each variable correctly and avoid confusing the variables.

Q: How do I check my answer to an algebraic equation? A: To check your answer, you can plug the value of the variable back into the original equation and verify that it is true.