Question

Find the minimum value of $x,$ if $5x+8\ge 3x.$

Answer 1

Given, $5x+8\ge 3x$

Step 1: Subtract both sides of the inequality by 8 to eliminate 8 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.
$5x+8-8\ge 3x-8$
$\Rightarrow 5x\ge 3x-8$

Step 2: Subtract both sides of the inequality by $3x$ to eliminate $3x$ 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.
$5x-3x\ge 3x-8-3x$
$\Rightarrow 2x\ge -8$

Step 3: Divide both sides of the inequality by 2.
Also, dividing both sides of the inequality by a positive number does not change the direction of the inequality.
$\frac{2x}{2}\ge \frac{-8}{2}$
$\Rightarrow x\ge -4$

So, the value of $x,$ which is greater than or equal to -4 satisfies the given inequality.

Hence, minimum value of the $x$ is $-4.$