SOLUTION: I HOPE U CAN HELP ME WITH THIS....SOLVE THE EQUATION AND INEQUALITIES. WRITE THE SOLUTION TO THE INEQUALITIES IN INTERVAL NOTATION. THANK U. A) 2|3-P|-4=2 B) 2|3-P|-4<2

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A)


Start with the given equation


Add 4 to both sides.


Divide both sides by 2



Break up the absolute value (remember, if you have , then or )

or Set the expression equal to the original value 3 and it's opposite -3




Now lets focus on the first equation


Subtract 3 from both sides


Combine like terms on the right side


Divide both sides by -1 to isolate p



Divide

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Now lets focus on the second equation



Subtract 3 from both sides


Combine like terms on the right side


Divide both sides by -1 to isolate p



Divide





So the solutions to are:

or



Notice if we graph and (just set each side equal to y and graph), we get


Graph of (red) and (green)

and we can see the two graphs intersect at and . So this verifies our answer.

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Start with the given inequality


Add 4 to both sides.


Divide both sides by 2



Break up the absolute value (remember, if you have , then and )

and Break up the absolute value inequality using the given rule


Combine the two inequalities to get a compound inequality


Subtract 3 from all sides


Multiply all sides by -1 to isolate p. This will flip the inequality signs

Rearrange the inequality

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Answer:

So our answer is





which looks like this in interval notation





if you wanted to graph the solution set, you would get
Graph of the solution set in blue and the excluded values represented by open circles