Question 502706: (|5p + 7| / 2) + 2 = 7
Answer by persian52(161) (Show Source):
You can put this solution on YOUR website! ((|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|)/(2)*2=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).
(5p)/(5)=(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).
(5p)/(5)=-(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).
(5p)/(5)=-(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)
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