Math please |p minus 4|<9
| p - 4 | < 9
(p - 4) < 9 or (4 - p) < 9
p < 13 or -p < 5
p < 13 or p > -5
so
-5 < p < 13
the absolute value of p - 4 is p +4
so...
p + 4 < 9
subtract 4 from both sides
p < 5
Damon is right sorry....my answer is wrong
To solve the inequality |p - 4| < 9, we need to consider two cases: when p - 4 is positive, and when p - 4 is negative.
Case 1: p - 4 is positive
If p - 4 is positive, then the absolute value of (p - 4) is equal to (p - 4). So the inequality becomes (p - 4) < 9.
To isolate p, we can add 4 to both sides: (p - 4) + 4 < 9 + 4.
This simplifies to p < 13.
Case 2: p - 4 is negative
If p - 4 is negative, then the absolute value of (p - 4) is equal to -(p - 4). So the inequality becomes -(p - 4) < 9.
To solve this, we multiply both sides by -1, remembering to flip the inequality sign: -(-(p - 4)) > -9.
Simplifying, we have p - 4 > -9.
Next, we add 4 to both sides: (p - 4) + 4 > -9 + 4.
This simplifies to p > -5.
Combining the solutions from both cases, we find that p must satisfy both p < 13 and p > -5. This means that p must be between -5 and 13, but not including those values.
So, the solution to the inequality |p - 4| < 9 is -5 < p < 13.