-7x+4=2x-14

Let's solve the equation step by step:

Given: \[ -7x + 4 = 2x - 14 \]

Step 1: Get all the x terms on one side and constants on the other

Add \(7x\) to both sides: \[ -7x + 7x + 4 = 2x + 7x - 14 \] \[ 0 + 4 = 9x - 14 \] which simplifies to: \[ 4 = 9x - 14 \]

Step 2: Add 14 to both sides to isolate the term with \(x\): \[ 4 + 14 = 9x - 14 + 14 \] \[ 18 = 9x \]

Step 3: Divide both sides by 9 to solve for \(x\): \[ x = \frac{18}{9} = 2 \]

Final answer: \[ \boxed{x = 2} \]