Question

Find the solution set for the following inequation:
$x+\frac{5}{2}<-\frac{5}{2}+5x$; $xϵR$

• A. $x<2$
• B. $x>1.25$
• C. $x<1.25$
• D. $x<-2$

Answer 1

The correct option is B $x>1.25$

Given: $x+\frac{5}{2}<-\frac{5}{2}+5x$

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 given inequation.

$x-5x<-\frac{5}{2}-\frac{5}{2}$

$\Rightarrow -4x<-\frac{10}{2}$

$\Rightarrow -4x<-5$


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 dividing the above inequation with -4, we get

$\Rightarrow x>\frac{5}{4}$

$\Rightarrow x>1.25$