For what values of y does the binomial 3y−5 belong to the interval (−1; 1)?
No it didn't work
if (3y-5) = -1
3 y = 4
y = 4/3
if (3y-5) = +1
3 y = 6
y = 2
it is linear so anything between 4/3 and 2 should work, check with y = 5/3
3(5/3) - 5 = 0, yes
better way to put his answer is 4/3<y<2 because he is saying thats what y is equal two for the two equations
yes I may have just spelled to as two but I don't care
To determine the values of y for which the binomial 3y - 5 belongs to the interval (-1, 1), we need to solve the inequality:
-1 < 3y - 5 < 1
Let's solve it step by step:
Step 1: Add 5 to all parts of the inequality:
-1 + 5 < 3y - 5 + 5 < 1 + 5
4 < 3y < 6
Step 2: Divide all parts by 3 (the coefficient of y):
4/3 < 3y/3 < 6/3
4/3 < y < 2
So, the values of y that make the inequality true and therefore belong to the interval (-1, 1) are y ∈ (4/3, 2).