2-4(х-3)<7-3х

To solve the inequality \( 2 - 4(x - 3) < 7 - 3x \), follow these steps:

1. Distribute the \(-4\) on the left side: \[ 2 - 4x + 12 < 7 - 3x \] This simplifies to: \[ 14 - 4x < 7 - 3x \]

2. To isolate \(x\), first, add \(4x\) to both sides: \[ 14 < 7 - 3x + 4x \] Which simplifies to: \[ 14 < 7 + x \]

3. Next, subtract \(7\) from both sides: \[ 14 - 7 < x \] So, \[ 7 < x \] or equivalently, \[ x > 7 \]

The solution to the inequality is \(x > 7\).