Question
A student wrote the inequality "y" greater than 4 "x" minus 17y>4x−17. Her friend solved the inequality and said that ( 12 , 31 )(12,31)is one of the possible solutions of this inequality. Is her friend correct? 314 times 2 minus 17 314 times 2 minus 17 314 times 2 minus 17 314 times 2 minus 17
Answers
GPT-4o mini
To determine if the point \( (12, 31) \) is a solution of the inequality \( y > 4x - 17 \), we need to substitute \( x = 12 \) and \( y = 31 \) into the inequality.
1. **Substitute \( x \) into the equation \( 4x - 17 \)**:
\[
4(12) - 17 = 48 - 17 = 31
\]
2. **Now we replace \( y \) with 31 in the inequality**:
The inequality can be written as:
\[
31 > 31
\]
This statement is **not true**, since \( 31 \) is not greater than \( 31 \).
Thus, the point \( (12, 31) \) does not satisfy the inequality \( y > 4x - 17 \). Therefore, her friend is **not correct**.
1. **Substitute \( x \) into the equation \( 4x - 17 \)**:
\[
4(12) - 17 = 48 - 17 = 31
\]
2. **Now we replace \( y \) with 31 in the inequality**:
The inequality can be written as:
\[
31 > 31
\]
This statement is **not true**, since \( 31 \) is not greater than \( 31 \).
Thus, the point \( (12, 31) \) does not satisfy the inequality \( y > 4x - 17 \). Therefore, her friend is **not correct**.