3.2 If \( a=-2, b=3 a-1, c=-4-b \) and \( x=3+c \), determine the value of \( x \). 3.3 The sum of three consecutive integers are -75 . Calculate the value of the second integer.
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To find \( x \), we start by determining the value of \( b \). Given \( a = -2 \), we have: \[ b = 3a - 1 = 3(-2) - 1 = -6 - 1 = -7 \] Next, we find \( c \): \[ c = -4 - b = -4 - (-7) = -4 + 7 = 3 \] Finally, we calculate \( x \): \[ x = 3 + c = 3 + 3 = 6 \] Thus, the value of \( x \) is \( 6 \). For the second part, let the three consecutive integers be \( n - 1, n, n + 1 \). Their sum is: \[ (n - 1) + n + (n + 1) = 3n \] We know this sum equals \( -75 \): \[ 3n = -75 \] Solving for \( n \): \[ n = \frac{-75}{3} = -25 \] Thus, the second integer is \( -25 \).