Ask a New Question
Menu

Arrange the steps in order to solve x/4 > 5/9

1/4x/1/4 > 5/9/1/4
1/4x > 5/9
x > 20/9
x > 5/9*4/1
x > 2 2/9

3 answers

To solve the inequality \( \frac{x}{4} > \frac{5}{9} \), we can follow these steps in order:

  1. Start with the original inequality: \[ \frac{x}{4} > \frac{5}{9} \]

  2. Multiply both sides by 4 to eliminate the fraction: \[ x > \frac{5}{9} \times 4 \] This corresponds to step: \[ x > \frac{5}{9} \times \frac{4}{1} \]

  3. Calculate \( \frac{5 \times 4}{9} \): \[ x > \frac{20}{9} \] This corresponds to the step: \[ x > \frac{20}{9} \]

  4. Now, convert \( \frac{20}{9} \) into a mixed number: Since \( 20 \div 9 = 2 \) with a remainder of \( 2 \), we can express it as: \[ x > 2 \frac{2}{9} \] This corresponds to the step: \[ x > 2 \frac{2}{9} \]

So the correct order of steps to solve the inequality \( \frac{x}{4} > \frac{5}{9} \) is:

  1. \( \frac{x}{4} > \frac{5}{9} \)
  2. \( \frac{x}{4} \times 4 > \frac{5}{9} \times 4 \) (which simplifies to \( x > \frac{20}{9} \))
  3. \( x > \frac{20}{9} \)
  4. \( x > 2 \frac{2}{9} \)

The correct sequence is:

  1. \( \frac{x}{4} > \frac{5}{9} \)
  2. \( x > \frac{5}{9} \times 4 \)
  3. \( x > \frac{20}{9} \)
  4. \( x > 2 \frac{2}{9} \)
Should be 5 answers but the first one is 1/4x over 1/4 > 5/9 over 1/4

Thanks for the clarification! Let's arrange the steps correctly with the five answers you provided in the format you specified.

Given the inequality:

\[ \frac{x}{4} > \frac{5}{9} \]

Here’s how we can arrange the steps in order:

  1. Start with the inequality: \[ \frac{x}{4} > \frac{5}{9} \]

  2. Multiply both sides by \( \frac{1}{4} \) (or equivalently rearranging gives us the next step): \[ \frac{1}{4} x > \frac{5}{9} \cdot \frac{1}{4} \]

  3. Simplify the right side: \[ x > \frac{5 \cdot 4}{9 \cdot 1} = \frac{20}{9} \]

  4. Convert \( \frac{20}{9} \) to a mixed number to find: \[ x > 2 \frac{2}{9} \]

Using the steps you provided, here's the correct ordered sequence:

  1. \( \frac{x}{4} > \frac{5}{9} \)
  2. \( \frac{1}{4} x > \frac{5}{9} \cdot \frac{1}{4} \)
  3. \( x > \frac{5 \cdot 4}{1 \cdot 9} \) (or equivalently: \( x > \frac{20}{9} \))
  4. \( x > \frac{20}{9} \)
  5. \( x > 2 \frac{2}{9} \)

So, the entire sequence of steps to solve the inequality in your format correctly would be:

  1. \( \frac{x}{4} > \frac{5}{9} \)
  2. \( \frac{1}{4} x > \frac{5}{9} \cdot \frac{1}{4} \)
  3. \( x > \frac{20}{9} \)
  4. \( x > 2 \frac{2}{9} \)

Let me know if there's anything else you'd like to clarify!