Solve.
17x = 3
A. x = 0.18
B. x = 5.67
C. x = 14
D. x = 21
The Correct Answer and Explanation is :
The correct answer is: A. ( x = 0.18 )
To solve the equation ( 17x = 3 ), we need to isolate ( x ). Here’s the step-by-step process:
- Start with the equation:
[
17x = 3
] - Divide both sides by 17:
To isolate ( x ), we divide both sides of the equation by 17. This gives us:
[
x = \frac{3}{17}
] - Calculate the value:
Next, we perform the division:
[
x = 0.1764705882352941 \ldots
]
This can be rounded to ( x \approx 0.18 ).
Answer Selection
Looking at the provided options:
- A. ( x = 0.18 )
- B. ( x = 5.67 )
- C. ( x = 14 )
- D. ( x = 21 )
The correct answer is A. ( x = 0.18 ), as it is the closest approximation of ( \frac{3}{17} ).
Explanation of the Process
This equation exemplifies a basic algebraic manipulation where the goal is to isolate the variable ( x ). This process is fundamental in algebra and is widely applicable across different types of equations.
Understanding how to manipulate equations is crucial, not just for solving mathematical problems, but also for more complex applications in fields such as physics, engineering, and economics. For instance, in physics, one might encounter equations that require isolating a variable to find an unknown quantity, such as force or velocity.
The principle behind dividing both sides of the equation by the same non-zero number (in this case, 17) ensures that the equality remains valid. This is known as the property of equality. The importance of this principle cannot be overstated, as it forms the backbone of all algebraic problem-solving.
In summary, the correct solution to the equation ( 17x = 3 ) is ( x \approx 0.18 ), highlighting the straightforward yet powerful techniques employed in algebra.