To solve the equation \( 2(3x - 4) - 2x + 2 = 22 \), follow these steps:
-
Distribute the 2 across the terms inside the parentheses: \[ 2 \cdot 3x - 2 \cdot 4 = 6x - 8 \] So, the equation becomes: \[ 6x - 8 - 2x + 2 = 22 \]
-
Combine like terms on the left side: \[ (6x - 2x) + (-8 + 2) = 22 \] This simplifies to: \[ 4x - 6 = 22 \]
-
Add 6 to both sides to isolate the term with \(x\): \[ 4x - 6 + 6 = 22 + 6 \] This simplifies to: \[ 4x = 28 \]
-
Divide both sides by 4 to solve for \(x\): \[ x = \frac{28}{4} \] This simplifies to: \[ x = 7 \]
Thus, the solution is \( \boxed{7} \).