What must be added to $(5x + 4y)$ to get $(2x - 10y)$?

Set up the equation: ( 5 x + 4 y ) + A = ( 2 x − 10 y ) .
Isolate A : A = ( 2 x − 10 y ) − ( 5 x + 4 y ) .
Combine like terms: A = 2 x − 5 x − 10 y − 4 y .
Simplify to find the expression: − 3 x − 14 y ​ .

Explanation

Understanding the Problem We are given two expressions, ( 5 x + 4 y ) and ( 2 x − 10 y ) . Our goal is to find an expression that, when added to ( 5 x + 4 y ) , results in ( 2 x − 10 y ) . Let's call the expression we need to find A .

Setting up the Equation We can set up the equation as follows: ( 5 x + 4 y ) + A = ( 2 x − 10 y ) To find A , we need to isolate it on one side of the equation. We can do this by subtracting ( 5 x + 4 y ) from both sides: A = ( 2 x − 10 y ) − ( 5 x + 4 y )

Simplifying the Expression Now, let's simplify the expression for A by combining like terms: A = 2 x − 10 y − 5 x − 4 y Combine the x terms: 2 x − 5 x = − 3 x .
Combine the y terms: − 10 y − 4 y = − 14 y .
So, we have: A = − 3 x − 14 y

Final Answer Therefore, the expression that must be added to ( 5 x + 4 y ) to get ( 2 x − 10 y ) is − 3 x − 14 y .


So the final answer is: − 3 x − 14 y
Examples
This type of problem is useful in many real-world scenarios. For example, imagine you are managing a budget. You currently have expenses represented by ( 5 x + 4 y ) , where x is the cost of materials and y is the cost of labor. You want to reduce your expenses to ( 2 x − 10 y ) . The expression − 3 x − 14 y tells you how much you need to reduce each of those costs to meet your new budget goals. This kind of algebraic manipulation helps in planning and making informed decisions about resource allocation.

Answered by GinnyAnswer | 2025-07-03

To find what must be added to (5x + 4y) to obtain (2x - 10y), we set up the equation (5x + 4y) + A = (2x - 10y) and isolate A. After simplifying, we find that A = -3x - 14y. Thus, the expression to be added is -3x - 14y.
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Answered by Anonymous | 2025-07-04