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

Let E be the expression to add.
Set up the equation: ( 5 x + 4 y ) + E = ( 2 x − lo g ) .
Solve for E : E = ( 2 x − lo g ) − ( 5 x + 4 y ) .
Simplify: E = − 3 x − 4 y − lo g . The final answer is − 3 x − 4 y − lo g ​ .

Explanation

Understanding the Problem We are given two expressions: ( 5 x + 4 y ) and ( 2 x − lo g ) . We need to find an expression that, when added to ( 5 x + 4 y ) , results in ( 2 x − lo g ) .

Setting up the Equation Let the expression to be added be E . We can set up the equation: ( 5 x + 4 y ) + E = ( 2 x − lo g ) .

Isolating E To solve for E , we need to isolate it on one side of the equation. We can do this by subtracting ( 5 x + 4 y ) from both sides: E = ( 2 x − lo g ) − ( 5 x + 4 y ) .

Simplifying the Expression Now, we simplify the expression for E by distributing the negative sign: E = 2 x − lo g − 5 x − 4 y .

Combining Like Terms Next, we combine like terms: E = ( 2 x − 5 x ) − 4 y − lo g . This simplifies to E = − 3 x − 4 y − lo g .

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


Examples
Imagine you're balancing a budget. You currently have expenses represented by ( 5 x + 4 y ) , and you want your total expenses to be ( 2 x − lo g ) . The expression we found, ( − 3 x − 4 y − lo g ) , represents the adjustments you need to make to your current expenses to reach your desired total. This could involve cutting costs or finding new sources of income to offset your current spending. Understanding how to manipulate algebraic expressions helps in managing and adjusting financial plans.

Answered by GinnyAnswer | 2025-07-03

To find what needs to be added to ( 5 x + 4 y ) to get ( 2 x − y ) , we set up the equation and isolate the unknown. After simplification, the result is E = − 3 x − 5 y . This means adding − 3 x − 5 y to ( 5 x + 4 y ) yields ( 2 x − y ) .
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Answered by Anonymous | 2025-07-04