Solve the equation. [tex]y+3=-y+9[/tex]
Answer (2)
Add y to both sides: 2 y + 3 = 9 .
Subtract 3 from both sides: 2 y = 6 .
Divide both sides by 2: y = 3 .
The solution to the equation is 3 .
Explanation
Isolating the variable Let's solve the equation step-by-step. Our goal is to isolate the variable 'y' on one side of the equation.
Adding 'y' to both sides We start with the equation:
y + 3 = − y + 9
To get all the 'y' terms on one side, we add 'y' to both sides of the equation:
y + 3 + y = − y + 9 + y
This simplifies to:
2 y + 3 = 9
Subtracting 3 from both sides Now, we want to isolate the term with 'y'. To do this, we subtract 3 from both sides of the equation:
2 y + 3 − 3 = 9 − 3
This simplifies to:
2 y = 6
Dividing by 2 Finally, to solve for 'y', we divide both sides of the equation by 2:
2 2 y = 2 6
This gives us:
y = 3
Examples
Imagine you and a friend are saving money. You start with $3 and save $1 each week. Your friend starts with $9 but spends 1 e a c h w ee k . T h ee q u a t i o n y+3 = -y+9$ helps you determine after how many weeks (y) you both will have the same amount of money. Solving such equations is crucial in personal finance, budgeting, and understanding break-even points in business.
To solve the equation y + 3 = − y + 9 , we isolate y by first adding y to both sides, leading to 2 y + 3 = 9 . After subtracting 3 from both sides and dividing by 2, we find that y = 3 . The solution shows the value when both sides of the equation are equal.
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