Explanation And Solution Of "3Z 5 2Z 25 5Z" In Relaxed English Language

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Introduction

As a professional teacher, one of my roles is to help students understand complex topics in a simplified and relaxed manner. In this article, we will discuss the algebraic expression "3z 5 2z 25 5z" and provide a step-by-step solution to simplify it.

What is an Algebraic Expression?

Before we delve into the expression in question, it is important to understand what an algebraic expression is. Simply put, an algebraic expression is a combination of numbers and variables, usually connected by mathematical operations such as addition, subtraction, multiplication, and division.

Breaking Down the Expression

Now, let's take a look at the expression "3z 5 2z 25 5z" and break it down. We can see that it is a combination of three different terms: "3z", "2z", and "5z". Each of these terms contains a variable "z" multiplied by a coefficient (a number that multiplies the variable). Additionally, there are two constants, "5" and "25", which are added to the expression.

Combining Like Terms

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable and exponent. In this case, all three terms contain the variable "z", so we can combine them. To do this, we add the coefficients of the like terms and keep the variable unchanged. The coefficient of "3z" is 3, the coefficient of "2z" is 2, and the coefficient of "5z" is 5. Adding these coefficients gives us a total of 10. Therefore, the simplified expression is "10z".

Adding the Constants

Now that we have combined like terms, we can add the constants "5" and "25" to the simplified expression. This gives us a final answer of "10z + 30".

Checking Our Work

To ensure that our answer is correct, we can substitute a value for "z" and evaluate both the original expression and the simplified expression. For example, if we let "z" equal 2, the original expression would be: 3(2) + 5 + 2(2) + 25 + 5(2) = 6 + 5 + 4 + 25 + 10 = 50 The simplified expression would be: 10(2) + 30 = 20 + 30 = 50 Since both evaluations result in the same answer, we can be confident that our solution is correct.

Conclusion

In summary, the expression "3z 5 2z 25 5z" can be simplified to "10z + 30" by combining like terms and adding the constants. It is important to understand the concept of like terms and to check our work to ensure that our solution is accurate. As a professional teacher, my aim is to help students understand complex topics in a simplified and relaxed manner, and I hope that this article has achieved that goal.