\( 4 w-4 \geq 8 \) and \( 3 w+6 \leq 3 \) Write the solution in interval notation: If there is no solution, enter \( \varnothing \).

To solve the inequalities, let's tackle each one separately. 1. For the first inequality: \( 4w - 4 \geq 8 \) Adding 4 to both sides gives: \( 4w \geq 12 \) Dividing by 4 yields: \( w \geq 3 \) 2. For the second inequality: \( 3w + 6 \leq 3 \) Subtracting 6 from both sides gives: \( 3w \leq -3 \) Dividing by 3 results in: \( w \leq -1 \) Now, we have two conditions: - \( w \geq 3 \) - \( w \leq -1 \) These two conditions cannot be true simultaneously since one requires \( w \) to be at least 3 and the other requires it to be at most -1. Hence, there are no values of \( w \) that satisfy both inequalities. Therefore, the solution in interval notation is \( \varnothing \).