Question

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

• A. $x+7>5$
• B. $x-10<-14$
• C. $x+3<1$
• D. $x-15\le -17$

Answer 1

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.

$\left(A\right)x+7>5$
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.
$\Rightarrow x+7-7>5-7\Rightarrow x>-2$

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

$\left(C\right)x+3<1$
Subtract 3 from both sides of the inequality in order to remove the 3 on the left hand side.
$\Rightarrow x+3-3<1-3\Rightarrow x<-2$

$\left(D\right)x-15\le -17$
Add 15 to both sides of the inequality in order to remove the 10 on the left hand side.
$\Rightarrow x-15+15\le -17+15\Rightarrow x\le -2$

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