Answer :

Let us solve for x in each of the inequalities.

The first inequality.

[tex]5-2x<-3_{}[/tex]

subtracting 5 from both sides gives

[tex]5-2x-5<-3_{}-5[/tex][tex]-2x<-8[/tex]

finally, multiplying both sides by -2 reverse the direction of the inequality to give

[tex]-\frac{2x}{-2}>-\frac{8}{-2}[/tex][tex]\boxed{x>4}[/tex]

which is our answer!

The second inequality

[tex]-3\mleft(-5+x\mright)>3[/tex]

Dividing both sides by -3 gives

[tex]\frac{3(-5+x)}{-3}<\frac{3}{-3}[/tex][tex]\rightarrow(-5+x)<-1[/tex]

finally, adding -5 to both sides gives

[tex]-5+x+5<-1+5[/tex][tex]\begin{gathered} \rightarrow x<-1+5 \\ \boxed{x<4} \end{gathered}[/tex]

which is our answer!

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