Question

If $\frac{4(x+2)}{5}<10$ holds for all $x,$ then which of the following is true?

Answer 1

Given: $\frac{4(x+2)}{5}<10$

Multiplying both sides with 5, the sign of the inequality remains unchanged as 5 is a positive number.

$⟹\frac{4(x+2)}{5}\times 5<10\times 5$

i.e., $4(x+2)<50$

$⟹4x+8<50$

Subtracting 8 from both sides, we get:

$4x+8-8<50-8$

i.e., $4x<42$

Dividing both sides by 4, the sign of the inequality remains unchanged as 4 is a positive number.

$\therefore \frac{4x}{4}<\frac{42}{4}$

i.e., $x<\frac{21}{2}$