Question

In the inequality

$37\le -2x+1$, what is the appropriate order of steps needed to solve the inequality for $x$?

• A. Add $1$ to both sides, divide both sides by $2$, and flip the inequality sign to $\ge$.
• B. Subtract $1$ from both sides, divide both sides by $-2$, and flip the inequality sign to $\ge$.
• C. Add $1$ to both sides, divide both sides by $-2$, and keep the original inequality sign.
• D. Subtract $1$ from both sides, divide both sides by $2$, and keep the original inequality sign.

Answer 1

Answer: (B)

Subtract $1$ from both sides, divide both sides by $-2$, and flip the inequality sign to $\ge$.

Given inequality is $37\le -2x+1$

Subtract $1$ from both sides, we get

$37-1\le -2x+1-1$

$\Rightarrow 36\le -2x$

On dividing both sides by $-2$, we get

$\frac{36}{-2}\le -\frac{2x}{-2}$

$\Rightarrow -18\le x$

Subtract $11$ from both sides, divide both sides by $-2$ and flip the inequality sign.