Question 851085
I'm going to skip the steps to solving 4(w+8)+3w<42 since you already know how to solve. You should have the solution {{{w < -10/7}}}. Hopefully you have this solution. If not, then let me know and I'll show you how to get this.



Now onto the graph



To graph {{{w < -10/7}}}, you follow these steps



Step 1) Draw out a number line. It doesn't need to be too big, but make sure to include the numbers -5, -4, -3, ..., 3, 4, 5



Step 2) Plot the point {{{w = -10/7}}}. Because {{{-10/7=-1.42857}}} (roughly), you are plotting this point between -2 and -1 (somewhat close to the midway point -1.5). It doesn't have to be perfectly exact. Just get in the general vicinity and you should be fine.



Step 3) Turn this point you just plotted into an open circle. This is to exclude the endpoint {{{w = -10/7}}}. We exclude because there is NO line under the inequality sign.



Step 4) Shade to the left of the open circle. Do not fill in the open circle. We shade to the left because of the " < " sign.