Question 86335
Question:


Solve each of the following equations for x, and check your results.

2(x – 3) – 3(x + 5) = 3(x – 2) – 7


Answer:


2(x – 3) – 3(x + 5) = 3(x – 2) – 7


Remove the parenthesis by  mulitplying .....as follows...



2*x - 2*3 - 3*x - 3*5 = 3*x - 3*2 - 7



==> 2x - 6 - 3x - 15 = 3x - 6 - 7



==> 2x - 3x - 6 - 15 = 3x - 6 - 7



==> -x - 15 = 3x - 17



Add x on both sides of the expression.....




==> -x - 15  + x = 3x - 17  + x



==> -x + x - 15 = 3x + x - 7



==> 0 -15 = 4x -7



Add 7 on both sides....



==> -15 + 7 = 4x - 7 + 7




==> -8 = 4x



Divde both sides by 4




==> {{{ -8/4  = 4x/4 }}}



==> -2 = x




So the solution is x = -2




To check your answer, plugg the value of x in the given expression......



==> 2(-2 – 3) – 3(-2 + 5) = 3(-2 – 2) – 7



==> 2(-5) – 3(3) = 3(-4) – 7



==> -10 - 9 = -12 -7



==> -19 = -19




That when we substitute the value of x in the given expression, you can see that  in the left and right hand side you have got the same value...that is -19



That is your solution is correct


That the value x = -2 satisfies the given expression.




Hope you found the explanation useful...



Regards.




Praseena.