6|4p+2|-8<34 please help solve this.
6|4p+2|-8<34
6|4p+2| <34+8=42
|4p+2| < (42/6)=7
So solve for
|4p+2| < 7
which means
either
4p+2 < 7
or
-(4p+2)<7
Can you take it from here?
|4p+2| < 7
(4p+2)<7 or (4p+2)<-7
4 p < 5 or 4p <-9
p<5/2 or p>-9/4
-9/4<p<5/2
check, p = 0 for example
12-8<34, right checks
check, p = -2 for example
36-8 <34 checks
Thank You :)
To solve the inequality 6|4p+2|-8<34, we need to isolate the variable p.
First, let's simplify the expression inside the absolute value brackets:
6|4p+2|-8<34
6 * |4p+2| < 42
Next, divide both sides of the inequality by 6:
|4p+2| < 7
Now, we need to consider two separate cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: (4p+2) ≥ 0
If 4p+2 is greater than or equal to 0, we can simply remove the absolute value brackets:
4p+2 < 7
Subtract 2 from both sides of the inequality:
4p < 5
Divide both sides by 4:
p < 5/4
Case 2: (4p+2) < 0
If 4p+2 is negative, we need to reverse the inequality when removing the absolute value brackets:
-(4p+2) < 7
Distribute the negative sign:
-4p - 2 < 7
Add 2 to both sides of the inequality:
-4p < 9
Divide both sides by -4. Remember, when dividing/multiplying by a negative number, we need to reverse the inequality:
p > -9/4
To summarize, the solution to the inequality 6|4p+2|-8<34 is:
p < 5/4 or p > -9/4