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Question

Which one of the following inequalities is represented on this number line?

A
x+7>5
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B
x10<14
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C
x+3<1
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D
x1517
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Solution

The correct option is C x+3<1

There is an open circle at -2 with the line showing the numbers that are less -2. This means x<2.
Now, let's check all the options one by one.

(A) x+7>5
Subtract 7 from both sides of the inequality in order to remove the 7 on the left hand side.
Also, subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.
x+77>57x>2

(B) x10<14
Add 10 to both sides of the inequality in order to remove the 10 on the left hand side.
x10+10<14+10x<4

(C) x+3<1
Subtract 3 from both sides of the inequality in order to remove the 3 on the left hand side.
x+33<13x<2

(D) x1517
Add 15 to both sides of the inequality in order to remove the 10 on the left hand side.
x15+1517+15x2

Hence, x+3<1 is the correct option.


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