4 + (3/(2*n)) = -7
subtract 4 from both sides of the equation to get:
3/(2*n) = -11
multiply both sides of the equation by (2*n) to get:
3 = -11 * (2*n)
divide both sides of the equation by -11 to get:
-3/11 = 2*n
divide both sides of the equation by 2 to get:
n = -3/22
that's equivalent to n = -.136 rounded to 3 decimal places.
that's the solution to the equation.
n or x = -.136 will come up later on the graph so keep it in mind.
for graphing, you are not looking for an individual solution, but you are looking to see what the equation looks like for all possible values of n.
to graph it using graphing software, you need to change n to x because most graphing software graphs x on the horizontal axis and y on the vertical axis.
we'll start again and solve the equation for graphing.
start with 4 + (3/(2*n)) = -7
replace n with x to satisfy the graphing software.
you get 4 + 3/(2x) = -7
note that 2*x or 2*n is the same as 2x or 2n.
now you want to get everything on one side of the equation.
add 7 to both sides of the equation to get 4 + 3/(2x) + 7 = 0
combine like terms to get 11 + 3/(2x) = 0
rearrange the terms to get 3/(2x) + 11 = 0
this is a specific solution that we solved for above that got us x = -3/22 which is equivalent to x = -.136 rounded to 3 decimal places.
for graphing purposes, however, replace 0 with y and your equation becomes 3/(2x) + 11 = y which can also be shown as, and will be graphed as, y = 3/(2x) + 11.
so your equation for graphing is y = 3/(2x) + 11
the graph is shown below:
now back to that specific solution of n = -3/22 which was changed to x = -3/22 to satisfy the requirements of the graphing software and which had a decimal equivalent of x = -.136 rounded to 3 decimal places.
look on the graph and you will see that, when y = 0, x = -.136.
that's your specific solution that we solved for when we had the equation 3/(2x) = 11 = 0 before we replace 0 with y.
what the grpah says is that, when y = 0, s = -3/22 which is shown as x = -.136.
that equation can be solved again for x as shown below:
start with 3/(2x) + 11 = 0
subtract 11 from both sides of the equation to get 3/(2x) = -11
divide both sides of the equation by -11 and multiply both sides of the equation by 2 to get:
3/-11 = 2x
divide both sides of the equation by 2 to get:
3/-22 = x
this can also be shown as x = -3/22 which has the decimal equivalent of x = -.136 rounded to 3 decimal places.
the graph and the specific solution agree.