Solve the inequality and write the solution in interval notation when possible. Express numbers as integers or simplified fractions. \[ 1+7(y-2) \leq 4+7(2 y+9) \] In interval notation, the solution set is \( \square . \square \) \( (\square, \square) \) \( (\square, \square][\square, \square) \)

Solve the equation \( 1+7(y-2) \leq 4+7(2 y+9) \). Solve the inequality by following steps: - step0: Solve for \(y\): \(1+7\left(y-2\right)\leq 4+7\left(2y+9\right)\) - step1: Move the expression to the left side: \(1+7\left(y-2\right)-\left(4+7\left(2y+9\right)\right)\leq 0\) - step2: Calculate: \(-3+7\left(y-2\right)-7\left(2y+9\right)\leq 0\) - step3: Calculate: \(-80-7y\leq 0\) - step4: Move the constant to the right side: \(-7y\leq 0+80\) - step5: Remove 0: \(-7y\leq 80\) - step6: Change the signs: \(7y\geq -80\) - step7: Divide both sides: \(\frac{7y}{7}\geq \frac{-80}{7}\) - step8: Divide the numbers: \(y\geq -\frac{80}{7}\) The solution to the inequality \(1+7(y-2) \leq 4+7(2y+9)\) is \(y \geq -\frac{80}{7}\). In interval notation, the solution set is \([-\frac{80}{7}, \infty)\).