Finding Solutions to 4x + 60/x = 40 by Drawing a Suitable Line

[tgpnlyt7095]

Homework Statement

Draw the graph of y = 3x + 60/x - 35.
Range : x= 1.5 less than or equal to 10
y= 9.5 to 1
Find Gradient
**Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line.

Homework Equations

none

The Attempt at a Solution

The graph is drawn, Gradient is found, which is 10.
** i have solved the question ' Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line.' by other means but i just do not know where to draw a straight line at. how does this relate to y = 3x + 60/x - 35 ??

 

[rock.freak667]

The Attempt at a Solution

The graph is drawn, Gradient is found, which is 10.
** i have solved the question ' Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line.' by other means but i just do not know where to draw a straight line at. how does this relate to y = 3x + 60/x - 35 ??

You found the gradient at what point?

4x + 60/x = 40

What do you get if you subtract 35 from each side and then subtract x from each side?

 

[tgpnlyt7095]

You found the gradient at what point?

4x + 60/x = 40

What do you get if you subtract 35 from each side and then subtract x from each side?

sorry, my scale for the y-axis is 1cm per unit, and for the x axis, 2cm 2units.

i drew the tangent and gradient was drawn from ( 1.4, 7 ) all the way down to ( 1.4 , -3 )
Rise / Run = 10/1 = 10.

 

[rock.freak667]

sorry, my scale for the y-axis is 1cm per unit, and for the x axis, 2cm 2units.

i drew the tangent and gradient was drawn from ( 1.4, 7 ) all the way down to ( 1.4 , -3 )
Rise / Run = 10/1 = 10.

Once you had two points to use.

For the second part, did you do what I suggested?

 

[tgpnlyt7095]

Once you had two points to use.

For the second part, did you do what I suggested?

where wouldn't be any changes even if i have done so isn't it ? 4x + 60/x = 40
4x + 60/x - 35 - x = 40-35-x
i still ended up with 4x + 60/x = 40.

 

[rock.freak667]

where wouldn't be any changes even if i have done so isn't it ? 4x + 60/x = 40
4x + 60/x - 35 - x = 40-35-x
i still ended up with 4x + 60/x = 40.

No from here 4x + 60/x - 35 - x = 40-35-x

you end up with

3x+ 60/x - 35 = 5-x


Now say you had to solve x³ = x, you can solve it using algebra or you can do it graphically. There will be a solution where the graph of the left side intersects the graph of the right side i.e. where y=x³ and y=x intersect.

So in your question, what graphs do you need to draw?

 

[tgpnlyt7095]

No from here 4x + 60/x - 35 - x = 40-35-x

you end up with

3x+ 60/x - 35 = 5-xNow say you had to solve x³ = x, you can solve it using algebra or you can do it graphically. There will be a solution where the graph of the left side intersects the graph of the right side i.e. where y=x³ and y=x intersect.

So in your question, what graphs do you need to draw?

im only required to draw the y = 3x + 60/x - 35 graph
am i required to simplify 3x+ 60/x - 35 = 5-x further??

 

[rock.freak667]

im only required to draw the y = 3x + 60/x - 35 graph

am i required to simplify 3x+ 60/x - 35 = 5-x further??

Did you understand what I typed?

You started with 4x + 60/x = 40. You did not draw this graph.

So from each side you subtracted (35+x) and got

4x + 60/x -35 - x = 40 -35 - x

which came out as

3x + 60/x -35 = 5 - x

So solutions for this equation will be the same as the solutions for 4x + 60/x = 40.

The graph of the left side is y=3x + 60/x -35. If you draw the graph of the right side on the same page, you will get the solutions you want.