7x 1 2 2 14x - 28

Apuntes

• Subtopic: [Inequality Solution Steps] To solve the inequality \(7x + 2 \leq 14x - 28\), we start by isolating \(x\). First, we rearrange the terms: \[ 9x + 2 = 14 \] Next, we subtract \(14x\) from both sides: \[ 9x - 14x \leq -28 - 2 \] This simplifies to: \[ -5x \leq -30 \] Now, we divide both sides by \(-5\). Remember that when dividing by a negative number, we must reverse the inequality sign: \[ x \geq \frac{-30}{-5} \] Thus, we find: \[ x \geq 6 \] The solution in interval notation is: \[ [6, \infty) \]