To solve the inequality \( \frac{1}{4}x - \frac{3}{4} > 5\frac{1}{4} \), follow these steps:
1. First, convert \( 5\frac{1}{4} \) to an improper fraction:
\[ 5\frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \]
2. Rewrite the inequality with the improper fraction:
\[ \frac{1}{4}x - \frac{3}{4} > \frac{21}{4} \]
3. To eliminate the fractions, multiply every term of the inequality by 4:
\[ 4 \left( \frac{1}{4}x - \frac{3}{4} \right) > 4 \left( \frac{21}{4} \right) \]
\[ x - 3 > 21 \]
4. Add 3 to both sides to isolate \( x \):
\[ x - 3 + 3 > 21 + 3 \]
\[ x > 24 \]
So, the solution to the inequality is \( x > 24 \).
The correct answer is:
A. \( x > 24 \)
Solve 1/4x - 3/4 > 5 1/4.
A. x > 24
B. x > 1 1/2
C. x > 18
D. x > 21 3/4
1 answer