Problem 25 - Algebra 1

Question

\(\frac{6.3}{x}\) when \(x=3\)

Step-by-Step Solution

Answer

The result is 2.1.

Step 1: Identify the problem

We are given the equation \(\frac{6.3}{x}\) and the value of \(x=3\). The problem is to find the value of this equation when \(x\) is equal to 3.

Step 2: Substitute the value of \(x\)

We can substitute the value of \(x\) into the equation. The new equation becomes \(\frac{6.3}{3}\).

Step 3: Solving the equation

Dividing 6.3 by 3 we get the value of 2.1.

Key Concepts

Understanding Fractions

Fractions represent a part or a segment of a whole. They consist of two numbers, one on top of the other, separated by a line: the numerator (top number) and the denominator (bottom number). In the given exercise, the fraction \( \frac{6.3}{x} \) shows 6.3 as the numerator and \( x \) as the denominator. When working with fractions:

• The numerator shows how many parts you actually have.
• The denominator shows how many equal parts the whole is divided into.

Knowing how to handle fractions is crucial in solving equations where division is involved. Fractions are not just "a part" of division problems, but they essentially are the division described by the top and bottom numbers.

Basics of Equation Solving

Equation solving is the process of finding the value of a variable that makes an equation true. In simple terms, it means "unveiling" the mystery number that you need to put into the equation to balance both sides. Take the exercise given: \( \frac{6.3}{x} \) with \( x = 3 \). By substituting the value given, you transform the equation to \( \frac{6.3}{3} \).

• Understand the equation and identify known values (here, \( x = 3 \)).
• Substitute these known values into the equation.
• Perform the arithmetic operations to solve the equation.

Finally, once you’ve completed the calculation, you’ve essentially "solved" the equation, arriving at the number that fits the conditions set by your equation.

Utilizing the Substitution Method

The substitution method involves taking known values of variables and replacing those variables to simplify the equation. This method helps you "test" and verify if your replacements give a valid solution. In the problem above, substitution plays a vital role.

• Start with identifying what needs substitution—in this case, the variable \( x \).
• Replace \( x \) with its given value in the original fraction equation: Transform \( \frac{6.3}{x} \) into \( \frac{6.3}{3} \).
• After substitution, solve the simplified equation to find your answer, which is 2.1 for this exercise.

The substitution method simplifies complex problems by making them more straightforward through known values, making calculations easier and more intuitive.