Math Problem Statement

translate to an equation:A number is subtracted from ten and that result is multiplied by four. This result is then divided by three more than the number. The entire result is equal to six.

Solution

Let's break this down step by step:

  1. "A number is subtracted from ten": Let the number be xx, so this expression becomes 10x10 - x.
  2. "That result is multiplied by four": This becomes 4(10x)4(10 - x).
  3. "This result is then divided by three more than the number": This expression becomes 4(10x)x+3\frac{4(10 - x)}{x + 3}.
  4. "The entire result is equal to six": This gives us the final equation.

So, the equation is:

4(10x)x+3=6\frac{4(10 - x)}{x + 3} = 6

Would you like me to solve this equation for xx or provide a further explanation?

Here are 5 related questions:

  1. How do you solve rational equations like the one above?
  2. What does it mean to cross-multiply in this context?
  3. Can this equation have multiple solutions?
  4. What happens if the denominator is zero?
  5. How would the equation change if the final result was not 6 but some other number?

Tip: When solving equations with fractions, always check for values that make the denominator zero (undefined points).

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Equations

Formulas

\frac{4(10 - x)}{x + 3} = 6

Theorems

Properties of Rational Equations

Suitable Grade Level

Grades 8-10