solve the inequality
|2y-5|>8
what will be the solution in interval notation
Something that helped me determine whether to set up a double inequality versus separate inequalities...
|expression|< k
less thAN (and)= double inequalities
-k<|expression|< k
|expression|> k
greatOR (or) = separate inequalities
|expression|< -k or |expression|> k
here's a link for further assistance:
http://www.algebralab.org/lessons/lesson.aspx?file=algebra_absolutevalueinequalities.xml
[2x - 5] > 8.
Since the number inside the absolute
value brackets can be positive or negative,we'll have 3 solutions:
+-(2x - 5) > 8,
Solve for positive value:
+(2x - 5) > 8,
2x - 5 > 8,
2x > 8 + 5,
2x > 13,
x > 13/2.
Solve for negative value:
-(2x - 5) > 8,
-2x + 5 > 8,
-2x > 8 - 5,
-2x > 3,
x < -3/2.
Solution set: x < -3/2, and x > 13/2.
CORRECTION: We'll have 2 solutions, NOT
3.
To solve the inequality |2y - 5| > 8, we need to isolate the absolute value expression and consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: (2y - 5) > 8
Solve the inequality as normal:
2y - 5 > 8
Add 5 to both sides:
2y > 13
Divide both sides by 2:
y > 6.5
Case 2: -(2y - 5) > 8
Flip the inequality sign when multiplying or dividing by a negative number:
-2y + 5 > 8
Subtract 5 from both sides:
-2y > 3
Divide both sides by -2 and remember to flip the inequality sign:
y < -1.5
Combining both cases, we get:
y < -1.5 or y > 6.5
Therefore, the solution to the inequality in interval notation is (-∞, -1.5) ∪ (6.5, +∞).