SOLUTION: Please help me solve the following two questions: {{{(2x-4)+5 = -7x-9}}} and {{{5/2 = 25/x}}}

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please help me solve the following two questions: {{{(2x-4)+5 = -7x-9}}} and {{{5/2 = 25/x}}}      Log On


   



Question 79732: Please help me solve the following two questions:
%282x-4%29%2B5+=+-7x-9
and
5%2F2+=+25%2Fx

Answer by erimir(14) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start by solving equation #1.
%282x-4%29%2B5=-7x-9
2x-4%2B5=-7x-9 {removing parentheses}
2x%2B1=-7x-9 {-4+5=1}}}
2x%2B7x=-9-1 {moving +1 from left side to right side, negating the element (+1 ==> -1), and moving +7x from right side to left side, negating this element too (-7x ==> 7x)}
9x+=+-10 {2x+7x=9x and -9-1=-10}}}
x+=+-10%2F9 {diving everything by 9 to get the value of x}


Then equation #2, which is a little bit more complicated:
5%2F2+=+25%2Fx
Now, to get rid of the fractions (a fraction is when you have a number over another, as for example 5%2F2 or x%2F2), we need to find the common denominator. This is an important step. Now we look at what is in the fractions where we find the denominator. On the left side of the equation, this is 2. On the right side, it is x. The common denominator may be found by multiplying these two numbers, and we get 2x. Now let us multiply each of the fractions by 2x.
%285%2F2%29%2A2x+=+%2825%2Fx%29%2A2x
%285%2A2x%29%2F2+=+%2825%2A2x%29%2Fx
10x%2F2+=+50x%2Fx
5x+=+50 {diving 10x by 2 = 5x, and 50x by x gives 50}
x+=+10 {diving each side by 5, giving us the final answer}}}
If you insert the value of x into the equation you may control that the answers are correct.
Cheers,
Eric