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## What is the value of x, when -9(x - 5) = x + 22 1/2

Hi Mikhail,

You have 2 parts to this problem. On the left side of the equation its -9(x-5) that is going to be -9x+45

on the right side of the equation you have x + 22 1/2,

converting 22 1/2 to an improper fraction is multiplication of the denominator by the whole number and then adding the numerator to give (2*22)+1. That means the right side of the equation is x + 45/2.

now you can multiply both sides by 2 to get

-18x + 90 = 2x + 45

next, subtract 2x and 90 from both sides to get

-20x = -45

so that x = 45/20 = 9/4 or 2 1/4

Plug it back into the original equation to check and you'll find:

-9[(9/4)-5] = 9/4 +90/4

-81/4+180/4 = 99/4

99/4 = 99/4

-9(x - 5) = x + 22 1/2, solution x=45/20 or x=2 1/4 step by step solution: step 1: change mix fraction to a pure fraction, 22 1/2 = [(22*2)+1]/2 =45/2 then -9(x - 5) = x + 22 1/2 ==> -9(x - 5) = x + 45/2 step 2: multiply the whole equation by 2, that is to write the equation without fraction or on linear form. -9(x - 5) = x + 45/2 ==> 2[-9(x - 5)] = 2[x + 45/2] ==> -18(x - 5) = 2x + 45 step 3: multiply by -18 to eliminate parentesis -18(x - 5) = 2x + 45 ==> -18x -5*-18 = 2x + 45 ==> -18x+90=2x+45 step 4: reagruping similar terms.To do this add the whole equation 18x-45 -18x+90=2x+45 ==> 18x-18x+90=18x+2x+45 ==> 90=20x+45 ==> -45+90=20x+45-45 ==> 45=20x step 5: to eliminate de 20 from 20x you have to divide by 20 the whole equation 45=20x ==> 45/20=20x/20 ==> 45/20=x or x=2 1/4 =========================================================================== That is:-9(x - 5) = x + 22 1/2 -9(x-5)=x+45/2 ==> -18(x-5)=2x+45 ==> -18x+90=2x+45 ==>

90-45=2x+18x ==> 45=20x ==> x=45/20 or x=2 1/4