Solve
|4y – 3| > 8
solution one: assume 4y-3 is positive.
4y-3>8
4y>11
y>11/4
solution two:
assume 4y-3 is negative.
3-4y>8
4y<-5
y<-5/4
To solve the inequality |4y - 3| > 8, we need to consider two cases:
Case 1: (4y - 3) > 8
In this case, we solve the inequality 4y - 3 > 8 by adding 3 to both sides of the inequality:
4y - 3 + 3 > 8 + 3
4y > 11
Finally, divide both sides of the inequality by 4 to isolate y:
4y / 4 > 11 / 4
y > 11/4
Case 2: -(4y - 3) > 8
In this case, we solve the inequality -(4y - 3) > 8 by multiplying both sides by -1, which reverses the inequality:
-1 * -(4y - 3) > -1 * 8
4y - 3 < -8
Next, add 3 to both sides of the inequality:
4y - 3 + 3 < -8 + 3
4y < -5
Divide both sides of the inequality by 4 to isolate y:
4y / 4 < -5 / 4
y < -5/4
Combining the solutions from both cases, we find that the solutions to the inequality |4y - 3| > 8 are:
y > 11/4 or y < -5/4