\( 3.26 ; 2 x+1 \) and \( 3 x-3 \) are the first three terms of a linear pattern. Calculate the value of \( x \).

To find the value of \( x \) in the linear pattern defined by the terms \( 3.26 \), \( 2x + 1 \), and \( 3x - 3 \), we must ensure that the differences between consecutive terms are equal. First, let's find the difference between the first two terms: \[ \text{Difference}_1 = (2x + 1) - 3.26 \] Next, we compute the difference between the second and third terms: \[ \text{Difference}_2 = (3x - 3) - (2x + 1) \] Setting these two differences equal gives us the equation: \[ (2x + 1) - 3.26 = (3x - 3) - (2x + 1) \] Expanding both sides: \[ 2x + 1 - 3.26 = 3x - 3 - 2x - 1 \] \[ 2x - 2.26 = x - 4 \] Solving for \( x \): \[ 2x - x = -4 + 2.26 \] \[ x = -1.74 \] Thus, the value of \( x \) is approximately \(-1.74\).