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Solve the equation for x

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3 Answers

Hi Theresa;
8(x-5)+x=9(x-5)+5
Let's combine as much as possible...
8x-40+x=9x-45+5
9x-40=9x-40
Let's cancel -40...
9x-40=9x-40
9x=9x
Let's cancel 9...
9x=9x
x=x
8(x-5) + x = 9(x-5) + 5
 
Distribute through.
8x - 40 + x = 9x - 45 + 5
 
Combine like terms.
8x + x - 40 = 9x - 45 + 5
 
9x - 40 = 9x -40
 
Add 40 to both sides.
 
9x = 9x
 
Subtract 9x from both sides.
 
0 = 0
 
 
Solution is true for all real numbers.
 
(-∞, ∞)
The problem with the recipe  "PEMDAS "  is that you should know that it's really "LPEMDAS" where the "L" stands for look!
8(x-5)+x=9(x-5)+5  subtract 5 from both sides and have
8(x-5)+x-5=9(x-5) or that 8(x-5)+(x-5)=9(x-5) or that 9(x-5)=9(x-5) an identity.  It holds for all numbers.