Question

select the correct answer. if ( 5(4 - x) < y + 12 ) and ( y + 12 < 3x + 1 ), then which statement is true? ( 3x + 1 - 5(4 - x) = y + 12 ) ( 5(4 - x) < 3x + 1 ) ( 5(4 - x) + 3x + 1 = y + 12 ) ( 3x + 1 < 5(4 + x) )

Explanation:

Step1: Recall the Transitive Property of Inequalities

The transitive property of inequalities states that if \( a < b \) and \( b < c \), then \( a < c \).

Step2: Identify the Given Inequalities

We are given \( 5(4 - x) < y + 12 \) and \( y + 12 < 3x + 1 \). Here, let \( a = 5(4 - x) \), \( b = y + 12 \), and \( c = 3x + 1 \).

Step3: Apply the Transitive Property

Using the transitive property with \( a < b \) and \( b < c \), we can conclude that \( a < c \), which means \( 5(4 - x) < 3x + 1 \).

Answer:

\( 5(4 - x) < 3x + 1 \) (the second option)