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Chapter 5: Problem 38

Solve. $$ \frac{x}{11}=\frac{7.1}{2} $$

Short Answer

Expert verified
x = 39.05

Step by step solution

01

- Set up the equation

The given equation is \ \( \frac{x}{11} = \frac{7.1}{2} \) \ We need to solve for \( x \).
02

- Cross-multiply

To eliminate the fractions, cross-multiply: \ \( x \cdot 2 = 11 \cdot 7.1 \). \ This will simplify to \ \( 2x = 78.1 \).
03

- Solve for x

Now, solve for \( x \) by dividing both sides by 2: \ \( x = \frac{78.1}{2} \) \ \( x = 39.05 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving equations
An equation is like a balance scale: whatever you do to one side, you must do to the other to keep it balanced. When solving equations, our goal is to isolate the unknown variable. Here鈥檚 a simple process:
  • Identify the variable you need to solve for.
  • Perform operations on both sides to isolate the variable.
In our example, the variable is \( x \). We start with the equation \( \frac{x}{11} = \frac{7.1}{2} \) and aim to find the value of x. By cross-multiplying, we eliminate the fractions and solve for \( x \) in the resulting equation.
fractions
Fractions represent parts of a whole and are written as \( \frac{numerator}{denominator} \).
  • The numerator (top part) shows how many parts we have.
  • The denominator (bottom part) shows how many equal parts the whole is divided into.
In our example, we have the fraction \( \frac{x}{11} \) and \( \frac{7.1}{2} \). To solve the equation involving fractions, cross-multiplication is an effective technique. Cross-multiplying involves multiplying the numerator of each fraction by the denominator of the other fraction and setting the products equal. This eliminates the fractions, making it simpler to find the unknown variable.
algebra
Algebra is a branch of mathematics that uses symbols (often letters) to represent numbers or quantities in formulas and equations. The symbols help us solve problems more generally than arithmetic does.
In our example, we solved \( \frac{x}{11} = \frac{7.1}{2} \) using algebraic techniques. Here鈥檚 how:
  • We eliminated the fractions by cross-multiplying: \( x \cdot 2 = 11 \cdot 7.1 \).
  • We simplified that to \( 2x = 78.1 \).
  • Finally, we isolated the variable \( x \) by dividing both sides by 2: \( x = \frac{78.1}{2} \). This gave us \( x = 39.05 \).
Understanding algebra allows us to solve equations and find unknown values efficiently, even when fractions are involved.

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