Let x be the cash Desmond is going to need, since he already has $5, the total amount he will need is:
[tex]x+5[/tex]and he wants this to be at least $50, hence we have the inequality:
[tex]x+5\ge50[/tex]Let's solve it:
[tex]\begin{gathered} x+5\ge50 \\ x\ge50-5 \\ x\ge45 \end{gathered}[/tex]Therefore he at least has to put $45 dollars more in his wallet, that is:
[tex]x\ge45[/tex]The solution in interval form is:
[tex]\lbrack45,\infty)[/tex]