\( 9 k \geq 0 \) or \( k+5<-3 \)

Solve the equation by following steps: - step0: Solve for \(k\): \(9k=0\) - step1: Rewrite the expression: \(k=0\) Solve the equation \( k+5=-3 \). Solve the equation by following steps: - step0: Solve for \(k\): \(k+5=-3\) - step1: Move the constant to the right side: \(k=-3-5\) - step2: Subtract the numbers: \(k=-8\) Let's solve the inequalities step by step. 1. **First Inequality: \( 9k \geq 0 \)** To solve this inequality, we can set it equal to zero to find the boundary point: \[ 9k = 0 \implies k = 0 \] Since \( 9k \) is greater than or equal to zero, \( k \) can be any value greater than or equal to 0. Thus, the solution for this inequality is: \[ k \geq 0 \] 2. **Second Inequality: \( k + 5 < -3 \)** We can solve this by isolating \( k \): \[ k + 5 = -3 \implies k = -3 - 5 \implies k = -8 \] Since this is a strict inequality, the solution is: \[ k < -8 \] ### Final Solution The overall solution to the compound inequality \( 9k \geq 0 \) or \( k + 5 < -3 \) is: - \( k \geq 0 \) or \( k < -8 \) This means \( k \) can take any value in the ranges \( (-\infty, -8) \) or \( [0, \infty) \).