An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Subtract 3 17 from both sides: subtraction property of equality.
Simplify the equation: simplification.
Subtract 2 1 x from both sides: subtraction property of equality.
Simplify the equation: simplification.
Multiply both sides by − 5 4 : multiplication property of equality.
Simplify to find the value of x: simplification. The solution is x = 15 8 .
Explanation
Problem Analysis We are given the equation 3 17 − 4 3 x = 2 1 x + 5 and asked to provide the justification for each step in its solution. The possible justifications are: addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality, and simplification.
Given Step 1: 3 17 − 4 3 x = 2 1 x + 5 is given.
Subtraction Property of Equality Step 2: 3 17 − 4 3 x − 3 17 = 2 1 x + 5 − 3 17 . We subtract 3 17 from both sides of the equation. This is justified by the subtraction property of equality.
Simplification Step 3: − 4 3 x = 2 1 x + 5 − 3 17 . We simplify the equation. Since 5 − 3 17 = 3 15 − 3 17 = − 3 2 , the equation becomes − 4 3 x = 2 1 x − 3 2 . This step is justified by simplification.
Subtraction Property of Equality Step 4: − 4 3 x − 2 1 x = 2 1 x − 3 2 − 2 1 x . We subtract 2 1 x from both sides of the equation. This is justified by the subtraction property of equality.
Simplification Step 5: − 4 3 x − 2 1 x = − 4 5 x . Thus, the equation becomes − 4 5 x = − 3 2 . This step is justified by simplification.
Multiplication Property of Equality Step 6: − 4 5 x ⋅ − 5 4 = − 3 2 ⋅ − 5 4 . We multiply both sides of the equation by − 5 4 . This is justified by the multiplication property of equality.
Simplification Step 7: x = 15 8 . This step is justified by simplification.
Examples
When solving equations in algebra, we often use properties of equality to isolate the variable. For example, if you're managing a budget and need to determine how much you can spend each month after accounting for fixed expenses, you might use the subtraction property of equality to subtract those fixed costs from your total income, helping you find the remaining amount available for discretionary spending. Similarly, if you're scaling a recipe and need to adjust ingredient quantities proportionally, you might use the multiplication property of equality to ensure the ratios remain consistent, maintaining the recipe's original flavor and balance.
The total charge delivered by the device is 450 coulombs, which corresponds to approximately 2.81 x 10^21 electrons flowing through it during 30 seconds at a current of 15.0 A.
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