Note that you are isolating the variable each time.
x - 7 > 10
Isolate the x. Add 7 to both sides
x - 7 (+7) > 10 (+7)
x > 10 + 7
x > 17
x > 17 is your answer
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3x ≤ 21
Isolate the x. Divide 3 from both sides
(3x)/3 ≤ (21)/3
x ≤ 21/3
x ≤ 7
x ≤ 7 is your answer
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5a - 2 < 18
Isolate the a. Add 2 to both sides
5a - 2 (+2) < 18 (+2)
5a < 20
Isolate the a. Divide 5 from both sides
5a/5 < 20/5
a < 20/5
a < 4
a < 4 is your answer
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2t + 8 ≥ -4(t + 1)
Follow PEMDAS. First, distribute -4 to all terms within the parenthesis
-4(t + 1) = -4(t) + (-4)(1) = -4t - 4
2t + 8 ≥ -4t - 4
Isolate the t. Subtract 8 and add 4t to both sides
2t (+4t) + 8 (-8) ≥ -4t (+4t) - 4 (-8)
2t + 4t ≥ -4 - 8
Simplify. Combine like terms
2t + 4t ≥ -4 - 8
6t ≥ - 12
Isolate the t. Divide 6 from both sides
(6t)/6 ≥ (-12)/6
t ≥ -12/6
t ≥ - 2
t ≥ - 2 is your answer
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~Rise Above the Ordinary