Answer:
[tex]$t<1$[/tex]
it seems that the answer didn't match the alternatives. But t < 1 is true.
If t > 1:
So, considering t = 2
[tex]$5-4(2)>\frac{3-2}{2} $[/tex]
[tex]$5-8>\frac{1}{2} $[/tex]
[tex]$-3>\frac{1}{2} $[/tex]
This is not true.
Step-by-step explanation:
Given inequality:
[tex]$5-4t>\frac{3-t}{2} $[/tex]
[tex]$2(5-4t)>\frac{3-t}{2} \cdot 2$[/tex]
[tex]$10-8t>3-t$[/tex]
[tex]$-8t+t>3-10$[/tex]
[tex]$-7t>-7$[/tex]
Dividing both sides by -7 will led to the flip of the inequality symbol.
[tex]$t<1$[/tex]
Considering t = -1
[tex]$5-4(-1)>\frac{3-(-1)}{2} $[/tex]
[tex]$5+4>\frac{3+1}{2} $[/tex]
[tex]$9>\frac{4}{2} $[/tex]
[tex]$9>2 $[/tex]
That's right
