Question

Solve 1/4x−3/4>5 1/4 .(1 point) Responses x>1/8 x>24 x>1 1/2 x >21 3/4

Answer 1

To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5 \frac{1}{4} \), first convert \( 5 \frac{1}{4} \) into an improper fraction:

\[
5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}
\]

Now replace \( 5 \frac{1}{4} \) in the original inequality:

\[
\frac{1}{4}x - \frac{3}{4} > \frac{21}{4}
\]

Next, add \( \frac{3}{4} \) to both sides:

\[
\frac{1}{4}x > \frac{21}{4} + \frac{3}{4}
\]
\[
\frac{1}{4}x > \frac{24}{4}
\]
\[
\frac{1}{4}x > 6
\]

Now, multiply both sides by \( 4 \) to eliminate the fraction:

\[
x > 24
\]

So the solution to the inequality is:

\[
x > 24
\]

The correct response is: **x > 24**.