Question

Solve the following inequation:
$-\frac{2}{3}<-\frac{x}{3}+1$.

• A. $5>x$
• B. $5<x$
• C. $53>x$
• D. $5\le x$

Answer 1

The correct option is A $5>x$

Given: $-\frac{2}{3}<-\frac{x}{3}+1$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

Now, subtracting 1 from both the sides
$\Rightarrow -\frac{2}{3}-1<-\frac{x}{3}$

$\Rightarrow -\frac{5}{3}<-\frac{x}{3}$

Rule: If both the sides of an inequation are multiplied or divided by the same negative number, then the sign of the inequality will get reversed.
On multiplying the above inequation by -1, we get

$\Rightarrow \frac{5}{3}>\frac{x}{3}$


Rule: If both the sides of an inequation are multiplied or divided by the same positive number, then the sign of the inequality will remain the same.
On multiplying both sides by 3 in the inequation;

$\Rightarrow 5>x$