Question

Match the following inequality with the solution.

• A. $x\le -2$
• B. $x\ge 13$
• C. $x\ge 4$
• D. $x\ge 14$

Answer 1

Before solving we need to remember the concept that adding or subtracting a number on both sides of the equation does not change the sign.
Now, let's take them one by one
A. $x+6\le 4$
Subtracting $6$ from both sides:
$\Rightarrow x+6-6\le 4-6$
$\Rightarrow x\le -2$

B. $x-8\ge 5$
Adding $8$ from both sides:
$\Rightarrow x-8+8\ge 5+8$
$\Rightarrow x\ge 13$

C. $9\le x+5$
Subgtracting with $5$ on both sides:
$\Rightarrow 9-5\le x+5-5$
$\Rightarrow 4\le x$
$\Rightarrow x\ge 4$

D. $6\le -8+x$
Adding $8$ on both sides:
$\Rightarrow 6+8\le -8+x+8$
$\Rightarrow 14\le x$
$\Rightarrow x\ge 14$