Solve the compound inequality. \[ 4 w+6 \geq 18 \text { and }-2 w<-12 \] Write the solution in interval notation: If there is no solution, enter \( \varnothing \). \[ \begin{array}{ll}\square & \infty\end{array} \]

To solve the compound inequality \( 4w + 6 \geq 18 \) and \(-2w < -12\), we can approach each part separately. First, solve \( 4w + 6 \geq 18 \): 1. Subtract 6 from both sides: \( 4w \geq 12 \) 2. Divide both sides by 4: \( w \geq 3 \) Next, solve \(-2w < -12\): 1. Divide both sides by -2, remembering to reverse the inequality sign: \( w > 6 \) Now, we need to combine the results. The solution to both inequalities must satisfy both conditions: From \( w \geq 3 \) and \( w > 6 \), the more restrictive condition is \( w > 6 \). In interval notation, the solution is: \[ (6, \infty) \]