Question

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

Answer 1

Should be 5 answers but the first one is 1/4x over 1/4 > 5/9 over 1/4

Answer 2

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. \( x > 2 \frac{2}{9} \)

Answer 3

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!