Solve for x 11/20=55/(20x)

Solution:

Step 1:

Express the equation in the form $\frac{11}{20} = \frac{55}{20x}$.

Step 2:

Identify and eliminate common factors between the numerator and denominator.

Step 2.1:

Extract the factor of $5$ from $55$ to get $\frac{5 \cdot 11}{20x} = \frac{11}{20}$.

Step 2.2:

Proceed to cancel out the common factors.

Step 2.2.1:

Take out the factor of $5$ from $20x$ to obtain $\frac{5 \cdot 11}{5 \cdot 4x} = \frac{11}{20}$.

Step 2.2.2:

Eliminate the common factor of $5$ to simplify to $\frac{11}{4x} = \frac{11}{20}$.

Step 2.2.3:

The equation now reads $\frac{11}{4x} = \frac{11}{20}$.

Step 3:

Cross-multiply to find $11 \cdot 20 = 4x \cdot 11$.

Step 4:

Isolate $x$ to solve the equation.

Step 4.1:

Rearrange the equation to $4x \cdot 11 = 11 \cdot 20$.

Step 4.2:

Begin simplification.

Step 4.2.1:

Compute $11 \cdot 4$ to get $44x = 11 \cdot 20$.

Step 4.2.2:

Calculate $11 \cdot 20$ to find $44x = 220$.

Step 4.3:

Divide both sides of $44x = 220$ by $44$ and simplify.

Step 4.3.1:

Divide $44x$ and $220$ by $44$ to get $\frac{44x}{44} = \frac{220}{44}$.

Step 4.3.2:

Simplify the left side of the equation.

Step 4.3.2.1:

Cancel out the common factor of $44$ to obtain $\frac{x}{1} = \frac{220}{44}$.

Step 4.3.2.2:

Simplify $x$ over $1$ to get $x = \frac{220}{44}$.

Step 4.3.3:

Simplify the right side of the equation.

Step 4.3.3.1:

Divide $220$ by $44$ to find $x = 5$.

Knowledge Notes:

The problem presents a proportion, which is an equation stating that two ratios are equal. To solve for $x$, we can use cross-multiplication, which is a method to solve proportions by multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other.

In this case, we have the proportion $\frac{11}{20} = \frac{55}{20x}$. To solve for $x$, we need to eliminate the common factors and then cross-multiply to isolate $x$.

The steps include:

1. Recognizing that both sides of the equation have a common factor that can be canceled out.

2. Factoring out the common factor and canceling it to simplify the equation.

3. Cross-multiplying to create an equation that can be solved for $x$.

4. Rearranging the equation and simplifying both sides to isolate $x$.

5. Dividing both sides of the equation by the coefficient of $x$ to find the value of $x$.

The solution involves basic algebraic manipulation, including factoring, canceling common factors, and solving linear equations.