Answer:
[tex] y > \frac{3}{17} [/tex]
Step-by-step explanation:
To solve this problem, simply set the binomial, [tex] 5y - 1 [/tex] as greater than [tex] \frac{3y - 1}{4} [/tex], and solve for the value of y as you would solve an equation.
Thus:
[tex] 5y - 1 > \frac{3y - 1}{4} [/tex]
Multiply both sides by 4
[tex] 4(5y - 1) > \frac{3y - 1}{4}*4 [/tex]
[tex] 4*5y - 4*1 > 3y - 1 [/tex]
[tex] 20y - 4 > 3y - 1 [/tex]
Subtract 3y from both sides
[tex] 20y - 4 - 3y > 3y - 1 - 3y [/tex]
[tex] 17y - 4 > -1 [/tex]
Add 4 to both sides
[tex] 17y - 4 + 4 > -1 + 4 [/tex]
[tex] 17y > 3 [/tex]
Divide both sides by 17
[tex] \frac{17y}{17} > \frac{3}{17} [/tex]
[tex] y > \frac{3}{17} [/tex]
Therefore, the value of y that will make the binomial [tex] 5y - 1 [/tex] greater than [tex] \frac{3y - 1}{4} [/tex] is [tex] y > \frac{3}{17} [/tex].
