Solve the equation. Express numbers as integers or decimals.
[tex]5.2 n+2.1=-3.1[/tex]
Answer (2)
To solve the equation 5.2 n + 2.1 = − 3.1 , we first subtract 2.1 from both sides to isolate 5.2 n , resulting in 5.2 n = − 5.2 . Next, we divide both sides by 5.2, giving us the solution n = − 1 .
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Subtract 2.1 from both sides: 5.2 n = − 5.2 .
Divide both sides by 5.2: n = − 1 .
The solution set is { − 1 } .
The final answer is − 1 .
Explanation
Understanding the Problem We are given the equation 5.2 n + 2.1 = − 3.1 and we need to solve for n . This is a linear equation, and we can isolate n by performing algebraic operations on both sides of the equation.
Subtracting 2.1 from both sides First, we subtract 2.1 from both sides of the equation to isolate the term with n :
5.2 n + 2.1 − 2.1 = − 3.1 − 2.1
Simplifying the equation Simplifying both sides, we get: 5.2 n = − 5.2
Dividing both sides by 5.2 Next, we divide both sides by 5.2 to solve for n :
5.2 5.2 n = 5.2 − 5.2
Finding the value of n Simplifying, we find the value of n :
n = − 1
Final Answer Therefore, the solution set is { − 1 } .
Examples
Linear equations are used in everyday life to calculate costs, distances, and other quantities. For example, if you know the cost of a taxi ride is a fixed fee plus a per-mile charge, you can use a linear equation to determine the total cost of a ride based on the distance traveled. Similarly, if you are saving money, you can use a linear equation to model your savings over time, predicting how much money you will have after a certain period.
