Solve the equation and check the solution.
[tex]3 w+8=44[/tex]
Answer (2)
To solve the equation 3 w + 8 = 44 , we find that w = 12 . We confirmed this by substituting w back into the original equation and checking our work. The solution is correct and validated.
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Subtract 8 from both sides of the equation: 3 w + 8 − 8 = 44 − 8 , which simplifies to 3 w = 36 .
Divide both sides by 3: 3 3 w = 3 36 , which simplifies to w = 12 .
Check the solution: 3 ( 12 ) + 8 = 36 + 8 = 44 , which is true.
The solution set is 12 .
Explanation
Understanding the Problem We are given the equation 3 w + 8 = 44 and we want to solve for w . This means we want to isolate w on one side of the equation.
Subtracting 8 from Both Sides First, we subtract 8 from both sides of the equation to isolate the term with w : 3 w + 8 − 8 = 44 − 8
Simplifying the Equation This simplifies to: 3 w = 36
Dividing by 3 Next, we divide both sides of the equation by 3 to solve for w :
3 3 w = 3 36
Finding the Value of w This simplifies to: w = 12
Checking the Solution Now, we check our solution by substituting w = 12 back into the original equation: 3 ( 12 ) + 8 = 44
Simplifying the Left Side Simplifying the left side, we get: 36 + 8 = 44
Verifying the Solution Which is true: 44 = 44
Stating the Solution Set Therefore, the solution set is {12}.
Examples
Imagine you're buying multiple items at a store, and there's a fixed shipping fee. This problem is similar to figuring out the cost of each item if you know the total cost, the number of items, and the shipping fee. For example, if you bought 3 books and paid a $8 shipping fee, totaling $44, you can use this equation to find the price of each book. This helps in budgeting, understanding costs, and making informed purchasing decisions.
