-x-(-2.5)-equivalent-expression.jpeg "(3-8y) X (-2.5) Equivalent Expression")
Exploring Equivalent Expressions: (3-8y) x (-2.5)
In mathematics, equivalent expressions are expressions that have the same value, even though they might look different. Let's explore how to find equivalent expressions for (3-8y) x (-2.5).
Understanding the Expression
The expression (3-8y) x (-2.5) involves:
- Parentheses: The parentheses indicate that we need to perform the operation inside them first.
- Multiplication: We are multiplying the expression (3-8y) by -2.5.
Finding Equivalent Expressions
We can find equivalent expressions by applying the distributive property of multiplication.
Distributive Property: a x (b + c) = (a x b) + (a x c)
Applying the distributive property to our expression:
(3-8y) x (-2.5) = (3 x -2.5) + (-8y x -2.5)
Simplifying:
(3 x -2.5) + (-8y x -2.5) = -7.5 + 20y
Therefore, an equivalent expression for (3-8y) x (-2.5) is -7.5 + 20y.
Why Equivalent Expressions Matter
Understanding equivalent expressions is essential for simplifying algebraic expressions and solving equations. By using the distributive property and other algebraic rules, we can manipulate expressions to make them easier to work with.
Example:
Let's say we want to solve the equation:
(3-8y) x (-2.5) = 15
Using the equivalent expression we found earlier, we can rewrite the equation as:
-7.5 + 20y = 15
This equation is much simpler to solve, allowing us to find the value of 'y'.
Conclusion
By applying the distributive property, we have successfully found an equivalent expression for (3-8y) x (-2.5). This process demonstrates the importance of understanding equivalent expressions in simplifying algebraic expressions and solving equations.