1
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Solve for x plus 8 is less than or equal to 6 and graph the solution

2
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So we have x plus 8 is less than or equal to 6

3
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So let's solve this inequality for x, and the easiest way to isolate an x on, let's isolate on the left

4
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hand side since it's already there is to just get rid of this 8,

5
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and the best way to get rid of this positive 8 is to subtract 8 from both sides

6
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So let's subtract 8 from both sides, that won't change the

7
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direction of the inequality, so the left hand side

8
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x plus 8 minus 8, you're just left with an x,

9
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the right hand side 6 minus 8 is negative 2, and we still have the less than or equal

10
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So we solve the inequality, we have x is less than or equal to

11
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negative 2, so let's draw that on a number line.

12
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So that's my number line, let's take 0 over here, maybe if

13
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we go 1, then we can go negative 1, negative 2, negative 3

14
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and we can keep going to the left, and we want

15
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all the x's that are less than or equal to negative 2

16
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since it can be equal to negative 2, we'll put a filled in

17
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line right here at negative 2, and all of the values less than that

18
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If it was just less than, if there wasn't the equal sign, we would have an open dot

19
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but since this is less than OR equal to, we've closed this dot

20
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Then we want all of the values below that

21
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And you can just sample a few and verify for yourself that they work,

22
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Based on this, negative 3 should work, and if you took

23
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negative 3, negative 3 plus 8 is five, which is definitely

24
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less than 6, so that works, and negative 1 shouldn't work,

25
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it's not included in this set over here, so let's try that out.

26
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Negative 1 plus 8 is 7, which is definitely not less than 6,

27
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so just sampling some points, it seems like we've got the right solution.