Question

Solve 1/4x−3/4>5 1/4.(1 point)
x>2/4
x>18
x 1/8 x > 21 3/4
x >1 1/2

Answer 1

there is no x >23

Answer 2

x>2/4
x>18
x 1/8 x > 21 3/4
x >1 1/2

Answer 3

To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5 \), we can follow these steps:

1. **Add \( \frac{3}{4} \) to both sides**:
\[
\frac{1}{4}x > 5 + \frac{3}{4}
\]

To add \( 5 \) and \( \frac{3}{4} \), we can convert \( 5 \) to a fraction with a denominator of \( 4 \):
\[
5 = \frac{20}{4}
\]
So,
\[
\frac{1}{4}x > \frac{20}{4} + \frac{3}{4} = \frac{23}{4}
\]

2. **Multiply both sides by \( 4 \)** (to eliminate the fraction):
\[
x > 23
\]

Thus, the solution to the inequality is:
\[
x > 23
\]

From the options you've given, the closest match is \( x > 21 \frac{3}{4} \). However, the exact solution is \( x > 23 \).

Answer 4

Let's solve the inequality step-by-step again to ensure we find the correct solution.

We want to solve the inequality:

\[
\frac{1}{4}x - \frac{3}{4} > 5
\]

1. **Add \(\frac{3}{4}\) to both sides**:
\[
\frac{1}{4}x > 5 + \frac{3}{4}
\]

First, we convert \(5\) into a fraction with a denominator of \(4\):
\[
5 = \frac{20}{4}
\]

Now adding:
\[
5 + \frac{3}{4} = \frac{20}{4} + \frac{3}{4} = \frac{23}{4}
\]

So, the inequality becomes:
\[
\frac{1}{4}x > \frac{23}{4}
\]

2. **Multiply both sides by \(4\)**:
\[
x > 23
\]

It seems I made an error initially by not properly addressing the solution set in the context of the provided options. If none of the options you provided match \(x > 23\), let me look closely at the possible options you've listed again:

- \(x > \frac{2}{4}\)
- \(x > 18\)
- \(x > \frac{21}{4}\)
- \(x > \frac{3}{2}\)

The closest response to the solution \(x > 23\) is indeed not in the provided options, but comparing \(x > 21 \frac{3}{4} (which is \frac{87}{4})\), if interpreted as greater, isn't an option.

### Conclusion
I'll recheck if they meant a surrounding range or other contextual adjustments beyond standard calculations. However, purely calculatively, the correct resolution remains:

\[
x > 23
\]

If you were to clarify any options or further parameters of consideration, feel free to let me know!

Answer 5

Thank you for your patience. Let's clarify the given options based on the solution we derived, which is \(x > 23\).

Here are the options you provided with simplified values where necessary:

1. \(x > \frac{2}{4}\) (which simplifies to \(x > \frac{1}{2}\))
2. \(x > 18\)
3. \(x > 21 \frac{3}{4}\) (which equals \(x > \frac{87}{4} = 21.75\))
4. \(x > 1 \frac{1}{2}\) (which equals \(x > \frac{3}{2} = 1.5\))

### Comparison with the derived solution \(x > 23\):

- **Option 1**: \(x > \frac{1}{2}\) is less than 23.
- **Option 2**: \(x > 18\) is less than 23.
- **Option 3**: \(x > 21 \frac{3}{4}\) is also less than 23.
- **Option 4**: \(x > 1 \frac{1}{2}\) is less than 23.

None of the provided options match the solution \(x > 23\).

### Clarifying the options:
If you were looking for which conditions are true or meet to come close to the derived answer, we identify that **none of those options satisfy \(x > 23\)**.

Typically in such contexts, option \(3\) \(x > 21 \frac{3}{4}\) ends up being the closest comparative scenario, if we would've to assume a possible selection on the most robust margin boundedly substantial toward 23.

If further clarifications or adjustments to options exist, do let me know!