1350=
660(1.075)
x
+350
The Correct Answer and Explanation is :
To solve the equation ( 1350 = 660(1.075)x + 350 ), we first need to isolate the variable ( x ). Here’s how we can do it step by step:
Step 1: Simplify the Equation
First, we can simplify the equation. Subtract 350 from both sides:
[
1350 – 350 = 660(1.075)x
]
This simplifies to:
[
1000 = 660(1.075)x
]
Step 2: Calculate ( 660(1.075) )
Now, we need to calculate ( 660(1.075) ):
[
660 \times 1.075 = 709.5
]
So we rewrite the equation as:
[
1000 = 709.5x
]
Step 3: Solve for ( x )
Next, we divide both sides by 709.5 to solve for ( x ):
[
x = \frac{1000}{709.5}
]
Calculating the right-hand side gives:
[
x \approx 1.4105
]
Conclusion
Thus, the solution to the equation ( 1350 = 660(1.075)x + 350 ) is approximately ( x \approx 1.4105 ).
Explanation
This equation represents a relationship where 1350 is equal to the product of 660 multiplied by ( 1.075 ) and ( x ), plus 350. It can be interpreted in various contexts, such as finance or physics, where linear relationships are essential.
The process of isolating ( x ) involved basic algebraic manipulations: first, moving constants to one side and then simplifying coefficients to derive ( x ). Multiplying 660 by 1.075 adjusted the original coefficient, reflecting some growth or adjustment (e.g., interest rate or inflation).
Once we had a clear coefficient for ( x ), we could solve for it directly by dividing. This approach showcases the foundational algebra skills necessary for solving linear equations, which are crucial in many fields, from mathematics and engineering to economics and data analysis. Understanding how to manipulate equations allows for the solving of real-world problems and the analysis of various scenarios efficiently.