Solve the following inequality: 2-3(x-4)lt 7x Write your answer as an interval and use INFTY for infty square

We are tasked with solving the inequality:<br /><br />\[<br />2 - 3(x - 4) < 7x<br />\]<br /><br />### Step 1: Expand and simplify<br />First, expand \( -3(x - 4) \):<br />\[<br />2 - 3x + 12 < 7x<br />\]<br /><br />Combine like terms on the left-hand side:<br />\[<br />14 - 3x < 7x<br />\]<br /><br />### Step 2: Isolate \( x \)<br />Add \( 3x \) to both sides to move all \( x \)-terms to one side:<br />\[<br />14 < 10x<br />\]<br /><br />Divide through by 10 to isolate \( x \):<br />\[<br />x > \frac{14}{10}<br />\]<br /><br />Simplify the fraction:<br />\[<br />x > \frac{7}{5}<br />\]<br /><br />### Step 3: Write the solution in interval notation<br />The solution is all values of \( x \) greater than \( \frac{7}{5} \). In interval notation, this is:<br />\[<br />\boxed{(\frac{7}{5}, \infty)}<br />\]