Explanation And Solution: Which Expression Is Equivalent To 5X+10Y-15?

Which expression is equivalent to 5x+10y15 The Equivalent from the-equivalent.com

Introduction

As a professional teacher, it is important to understand and explain mathematical concepts in a way that students can easily comprehend. In this article, we will discuss the expression 5x+10y-15 and explore its equivalent forms.

The Basics

Before we can dive into finding the equivalent expressions, we need to understand some basic concepts. In mathematics, an expression is a combination of numbers, variables, and operators. An operator is a symbol that represents a mathematical operation such as addition, subtraction, multiplication, or division.

Variables

Variables are letters that represent unknown quantities. In the expression 5x+10y-15, x and y are variables. The coefficient of the variable is the number that is multiplied by the variable. In this case, 5 is the coefficient of x and 10 is the coefficient of y.

Equivalent Expressions

Equivalent expressions are different expressions that have the same value for all values of the variables. In other words, they are different ways of writing the same expression. To find an equivalent expression, we need to use the properties of arithmetic operations.

Solution

To find the equivalent expression of 5x+10y-15, we can use the distributive property of multiplication over addition. The distributive property states that a(b+c) = ab + ac. We can apply this property to the given expression as follows: 5x+10y-15 = 5(x+2y-3) This is an equivalent expression because it has the same value for all values of x and y. We can check this by substituting values for x and y and comparing the results of the two expressions.

Explanation

The distributive property of multiplication over addition allows us to simplify expressions by distributing the multiplication over each term in the parentheses. In this case, we can factor out the common factor of 5 and apply the distributive property to get the equivalent expression.

Conclusion

In conclusion, the expression 5x+10y-15 is equivalent to 5(x+2y-3) using the distributive property of multiplication over addition. Equivalent expressions are useful in simplifying complex expressions and solving equations. As a teacher, it is important to explain these concepts clearly and provide examples to help students understand and apply them effectively.