Question

Solve the inequation: $\frac{x}{3}+5\le x+1$, where x $\in$ {4, 5, 6, 7}.

• A. {4, 5}
• B. {6, 7}
• C. Both A and B
• D. {-6, -7}

Answer 1

The correct option is B

{6, 7}

$\frac{x}{3}+5\le x+1$

Multiplying both sides by 3, we get:

or $3[\frac{x}{3}+5]\le 3(x+1)$

or $x+15\le 3x+3$

or $-2x\le -12$

Dividing both sides by -2, as the number is negative, so the sign of inequality is reversed.

or $\frac{-2x}{-2}\ge \frac{-12}{-2}$

or $x\ge 6$

but $x\in$ {4, 5, 6, 7}

Hence, the solution set is {6, 7}.