Question

Find the minimum value of $x,$ if $2x+16\le 10x$

Answer 1

Given, $2x+16\le 10x$

Step 1: Subtract both sides of the inequality by 16 to eliminate 16 on the left side of the equation.
Also, subtracting both sides of the inequality by the same number does not change the direction of the inequality.
$2x+16-16\le 10x-16$
$\Rightarrow 2x\le 10x-16$

Step 2: Subtract both sides of the inequality by $10x$ to eliminate 10x on the right side of the equation.
Also, subtracting both sides of the inequality by the same number does not change the direction of the inequality.
$2x-10x\le 10x-16-10x$
$\Rightarrow -8x\le -16$

Step 3: Divide both sides of the inequality by -8 to isolate x.
Also, dividing both sides of the inequality by a negative number changes the direction of the inequality.
$\frac{-8x}{-8}\ge \frac{-16}{-8}$
$\Rightarrow x\ge 2$

So, the value of $x,$ which is greater than or equal to 2 satisfies the given inequality.

Hence, minimum value of the $x$ is $2.$