Answer: 1 and 2
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Method 1)
Solve for x
11 > 2x + 5
11-5 > 2x
6 > 2x
2x < 6
x < 6/2
x < 3
So any x value smaller than 3 will be a solution. If we only consider values from the set {1,2,3,4}, then the solution values are {1,2}
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Method 2)
Plug each value from the set {1,2,3,4} into the original inequality. If you get a true statement after simplifying, then that value is a solution. Otherwise, it is not a solution.
Let's check x = 1
11 > 2x+5
11 > 2*1+5 ... replace x with 1
11 > 2+5
11 > 7 .... true statement since 11 is larger than 7
So x = 1 is a solution
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Let's check x = 2
11 > 2x+5
11 > 2*2+5
11 > 9 .. another true statement
x = 2 is another solution
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Let's check x = 3
11 > 2x+5
11 > 2*3+5
11 > 6+5
11 > 11 .. false, no number is larger than itself
x = 3 is not a solution
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Let's check x = 4
11 > 2x+5
11 > 2*4+5
11 > 8+5
11 > 13 ... false statement
x = 4 is not a solution
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We see that only x = 1 and x = 2 are solutions.