$3.5 y - 3.5 = 10.5$
Answer (1)
Add 3.5 to both sides of the equation: 3.5 y = 10.5 + 3.5 .
Simplify the equation: 3.5 y = 14 .
Divide both sides by 3.5 : y = 3.5 14 .
Solve for y : y = 4 .
Explanation
Understanding the Problem We are given the equation 3.5 y − 3.5 = 10.5 and our goal is to solve for y . This involves isolating y on one side of the equation by performing algebraic operations on both sides.
Adding 3.5 to Both Sides First, we add 3.5 to both sides of the equation to isolate the term with y :
3.5 y − 3.5 + 3.5 = 10.5 + 3.5
Simplifying the Equation This simplifies to: 3.5 y = 14
Dividing by 3.5 Next, we divide both sides of the equation by 3.5 to solve for y :
y = 3.5 14
Finding the Value of y Performing the division, we find: y = 4
Final Answer Therefore, the solution to the equation 3.5 y − 3.5 = 10.5 is y = 4 .
Examples
Imagine you're buying multiple items at a store, and there's a fixed discount applied to your total purchase. If you know the price per item and the total amount you paid after the discount, you can use a similar equation to figure out how many items you bought. For instance, if each item costs $3.5, and you had a discount of $3.5, and your final bill was $10.5, you can calculate the number of items you purchased using the given equation. This kind of problem-solving is useful in budgeting, shopping, and managing finances.
