Find the interval of all \(x\) such that \(\frac{-2x+5}{7}\) is in the interval [0,1).
We want to solve this
0 ≤ (-2x + 5) / 7 < 1 we can split this up as
0 ≤ (-2x + 5) / 7 and (-2x + 5) / 7 < 1
multiply both sides by 7
0 ≤ -2x + 5 -2x + 5 < 7
subtract 5 ftom both sides
-5 ≤ -2x -2x < 2
divide both sides by -2 and reverse the inequality signs
5/2 ≥ x x > -1
So....the solution is
-1 < x ≤ 5/2