Question 502706
((|5p+7|)/(2))+2=7

Remove the parentheses around the expression (|5p+7|)/(2).
(|5p+7|)/(2)+2=7

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
(|5p+7|)/(2)=-2+7

Add 7 to -2 to get 5.
(|5p+7|)/(2)=5

Multiply each term in the equation by 2.
(|5p+7|)/(2)*2=5*2

Cancel the common factor of 2 in the denominator of the first term (|5p+7|)/(2) and the second term 2.
(|5p+7|)/(<X>2<x>)*<X>2<x>=5*2

Reduce the expression by removing the common factor of 2 in the denominator of the first term (|5p+7|)/(2) and the second term 2.
|5p+7|*1=5*2

Multiply |5p+7| by 1 to get |5p+7|.
|5p+7|=5*2

Multiply 5 by 2 to get 10.
|5p+7|=10

Remove the absolute value term.  This creates a \ on the right-hand side of the equation because |x|=\x.
5p+7=\(10)

Set up the  portion of the \ solution.
5p+7=10

Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
5p=-7+10

Add 10 to -7 to get 3.
5p=3

Divide each term in the equation by 5.
(5p)/(5)=(3)/(5)

Cancel the common factor of 5 in (5p)/(5).
(<X>5<x>p)/(<X>5<x>)=(3)/(5)

Remove the common factors that were cancelled out.
p=(3)/(5)

Set up the - portion of the \ solution.
5p+7=-(10)

Multiply -1 by the 10 inside the parentheses.
5p+7=-10

Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
5p=-7-10

Subtract 10 from -7 to get -17.
5p=-17

Divide each term in the equation by 5.
(5p)/(5)=-(17)/(5)

Cancel the common factor of 5 in (5p)/(5).
(<X>5<x>p)/(<X>5<x>)=-(17)/(5)

Remove the common factors that were cancelled out.
p=-(17)/(5)

Multiply -1 by the 10 inside the parentheses.
5p+7=-10

Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
5p=-7-10

Subtract 10 from -7 to get -17.
5p=-17

Divide each term in the equation by 5.
(5p)/(5)=-(17)/(5)

Cancel the common factor of 5 in (5p)/(5).
(<X>5<x>p)/(<X>5<x>)=-(17)/(5)

Remove the common factors that were cancelled out.
p=-(17)/(5)

The solution to the equation includes both the positive and negative portions of the solution.
p=(3)/(5),-(17)/(5)