Which expression is equivalent to 2a+1/10a-5? This question takes center stage in this exploration of algebraic manipulation, equivalent expressions, and solving equations. Understanding equivalent expressions is a fundamental skill in mathematics, with applications in various fields. This article will delve into the intricacies of transforming expressions, uncovering the properties of equality, and demonstrating how to derive equivalent expressions.
In this comprehensive guide, we will embark on a step-by-step journey to isolate the desired expression, factoring out common factors from the denominator and simplifying the resulting expression by canceling out like terms. We will explore the nuances of solving equations, isolating the variable ‘a’ on one side of the equation, and discussing any potential restrictions or conditions that apply to the solution.
Equivalent Expressions
In mathematics, equivalent expressions are expressions that have the same value for all values of the variables involved. This concept is essential for solving equations, simplifying expressions, and understanding algebraic relationships.
Algebraic Manipulation
- To isolate the expression, we can start by multiplying both sides of the equation by 10a – 5, the denominator of the fraction on the left-hand side:
- 10a(2a + 1) = (10a – 5)(expression)
- 20a 2+ 10a = 10a(expression) – 5(expression)
- 20a 2+ 10a = 10a(expression) – 50 + 5(expression)
- 20a 2+ 10a = 10a(expression) + 5(expression) – 50
Equivalent Expressions
- To find equivalent expressions, we can use the following properties of equality:
- Reflexive property:Any expression is equivalent to itself.
- Symmetric property:If a = b, then b = a.
- Transitive property:If a = b and b = c, then a = c.
- Additive property:If a = b, then a + c = b + c.
- Multiplicative property:If a = b, then ac = bc.
Solving Equations, Which expression is equivalent to 2a+1/10a-5
To solve the equation 2a+1/10a-5 = expression for the variable ‘a’, we can isolate ‘a’ on one side of the equation by:
- Multiplying both sides by 10a – 5
- Simplifying the resulting equation
- Solving for ‘a’
Applications
Understanding equivalent expressions is beneficial in various real-world scenarios, including:
- Simplifying complex expressions
- Solving equations
- Deriving new expressions from existing ones
- Applying mathematical concepts to practical problems
Commonly Asked Questions: Which Expression Is Equivalent To 2a+1/10a-5
What is the first step in simplifying the expression 2a+1/10a-5?
Factor out the greatest common factor from the denominator, which is 5(2a-1).
How do you solve the equation 2a+1/10a-5 = 0?
Multiply both sides by 10a-5, then simplify and solve for ‘a’.
What are the potential restrictions on the solution to the equation 2a+1/10a-5 = 0?
The denominator cannot be zero, so 10a-5 cannot be equal to zero. Therefore, a cannot be equal to 1/2.
