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solve for x plus 8 is less than or equal to 6 and graph the solution so we have X plus 8 is less than or equal to 6 so let's solve this inequality for X and the easiest way to isolate an X on let's isolate on the left hand side since it's already there is to just get rid of this 8 and the best way to get rid of this positive 8 is to subtract 8 from both sides so let's subtract 8 from both sides that won't change the direction of the inequality so the left-hand side X plus 8 minus 8 you're just left with an X the right-hand side 6 minus 8 is negative 2 and we still have the less than or equal so we solve the inequality we have X is less than or equal to negative 2 so let's draw that on a number line so let's so that's my number line let's stick 0 over here maybe if we go 1 and then we could go negative 1 negative 2 negative 3 and we could keep going to the left and we want all the X's that are less than or equal to negative 2 since we're eat since it can be equal to negative 2 we'll put a filled-in line right here at negative 2 and all of the values less than that if it was just less than if there wasn't the equal sign we would have an open dot but since there's less than or equal to we've closed this dot and then we want all of the values below that all of the values below that and you could just sample a few and verify for yourself that they work based on this negative 3 should work and if you took negative 3 negative 3 plus 8 is 5 which is definitely less than 6 so that works and negative 1 shouldn't work it's not included in this set over here so let's try that out negative 1 negative 1 plus 8 is 7 which is definitely not less than 6 so just sampling some points it seems like we've got the right solution