Can someone help me solve a couple of inequalities? The first one to answer all 5 gets 10 points!?

Question

I don't get how to solve these 5 inequalities. Can you please show them to me how to, step by step? Please and thanks!

1. 12-m > 23
2. -25.9 -k > 6.1
3. 2>g+(-9)
4. 17 is less than or equal to -28 - u
5. -6 is less than or equal to d + 10

I also don't get 21t is less than or equal to -540. Thanks again for helping!

Answer 1

1. 12-m > 23
12-12-m > 23-12 minus 12 on both sides.
-m > 11 simplify.
-m/-1 < 11/-1 divide by -1 on both sides to make m positive. switch the inequality signs, since you are dividing with a negative.
m < -11 simplify.

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2. -25.9 -k > 6.1
-25.9 + 25.9-k > 6.1 + 25.9 add 25.9 on both sides
-k > 32 simplify
-k/-1 < 32/-1 divide by -1 on both sides
k < -32 simplify

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3. 2>g+(-9)
2>g-9 simplify
2+9>g-9+9 add 9 on both sides.
11>g simplify.
g<11 switch it around.

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4. 17 is less than or equal to -28 - u

17 _< -28-u (the _ means < with a line under it.)
17 + 28 _< -28 + 28 - u add on both sides
45 _< -u simplify
45/-1 _> -u/-1 divide by -1 on both sides, switch signs.
-45 _> u simplify
u _< -45 switch sides.

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5. -6 is less than or equal to d + 10

-6 _< d+10
-6-10_ -16 _ d_> -16 switch sides.

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6. 21t is less than or equal to -540

21t _< -540
21t/21 _< -540/21 divide by 21 on both sides
t _< -25.714.. simplify.