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

Question 134463: 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
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

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.

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

----------------------------------------------------

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
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