Solve 1/4x−3/4>5 1/4

Question

.(1 point)

x>2134
x greater than 21 ​Start Fraction 3 over 4 end fraction

x>18
x greater than 18

x>24
x greater than 24

x>112

Answer 1

To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5 \frac{1}{4} \), let's 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 the inequality becomes:

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

Next, we can add \( \frac{3}{4} \) to both sides to isolate the term with \( x \):

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

Combining the right side:

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

This simplifies to:

\[ \frac{1}{4}x > 6 \]

Now, we can multiply both sides of the inequality by \( 4 \) to solve for \( x \):

\[ x > 24 \]

So the solution to the inequality is:

\[ x > 24 \]

The correct answer is:

x > 24