3x - 4y > 7?

Question

How do I do this? A full working will be appreciated

This is an equation that says 3x minus 4y is greater than 7. How do i find out what x and y are?

Answer 1

3x-4y>7
add -3x
-4y>7-3x
multiply by -1
4y<3x-7
divide by 4
y<(3x-7)/4
plot the line as though it were 3x-4y=7
and then shade the right/correct side in keeping with the inequality

Answer 2

I'm assuming that you would like to plot this inequality.

You wish to shade a large section of the (x,y)-plane. Before we start, let's rearrange this inequality to one that may be easier to work with. Do this by subtracting 3x from both sides and then divide by -4. Because you are dividing by a negative number, your inequality (greater than) should change to the opposite inequality (less than). The result is:

y < (3/4)x - 7/4

This means that every selected point (x,y) will have a y-coordinate that is less than (3/4)*x - 7/4. You want to shade all such points. You should first find the boundary of your shaded region. That is defined by:

y = (3/4)x - 7/4

This is a straight line. This is a line with a positive slope of (3/4) that intersects the y-axis at -7/4. That is, you can plot a point (0,-7/4) and then rise 3 units in the y direction and run 4 units in the x direction and plot another point there. If you connect those two points, you have that line.

Draw the line on your graph with a dotted line. Because a strict inequality was used (i.e., greater than instead of greater than or equal to) then the line isn't included in your selected region of the graph, so you just dot the line to show the boundary but also indicate that the line is not included in your region.

Now, remember that we have:

y < (3/4)x - 7/4

That means that we need to shade everything "below" that line in the negative-y direction. That is, since it intersected the y-axis at -7/4, shade everything less than -7/4 on the y-axis and every point everywhere else in the plane that is on that side of the line.

The result is a slice of your (x,y)-plane that fills the bottom of your page.

Now let's test a point. Take a point that is clearly in this dark area. For example, take (5,-1):

3*5 - 4*(-1) = 15 + 4 = 19

19 is greater than 7, so this point should be included, so we shaded the correct reason.

I hope that helps.

Answer 3

Your x and y should be such that it satisfies the equation 3x-4y>7. But since there are two variables and only one equation, you can have infinite solutions to this equation.
Eg, assume y=m, a constant. then x should be such that x>(7+4m)/3. This is true for all values of y=m.

Answer 4

This equation can be rewritten as
y<(3/4)x-7/4
Draw a line such that it passes through (0,-7/4) and has a gradient of 3/4 i.e. the line goes up 3 units as it goes along 4 units.
Any corresponding values for x and y that lie beneath this line are valid and satisfy your inequality.

Answer 5

Solving for x

3x - 4y >7

3x - 4y + 4y > 7 + 4y

3x > 7 + 4y

3x/3 > 7/ 3 + 4y / 3

x = > 7/ 3 + 4y / 3

- - - - - - - - - - - - - - - - -

Solving for y

3x - 4y > 7

3x - 4y - 3x > 7 - 3x

- 4y > 7 - 3x

- 4y / -4 < 7 /-4 - 3x / -4

y < 7 / - 4 - 3x /- 4

Answer 6

gopal is right
x/2.33 - 4/1.75 =1
draw a graph with X and Y axes
mark co-ordinate 7/3= 2.33 on X axis

mark co-ordinate -7/4= -1.75 on Y axis
shade the area to the right,i.e away from the origin
the shaded area is represented by the inequation
best regards,

Answer 7

if x is greater than 5, and y = 2 then it would work.

Answer 8

3x - 4y > 7
3x > 7+4y
x > (4y+7)/3


Doug

Answer 9

cud be owt

as long as 3x-4y is greater than 7

i think

Answer 10

Do what? There's not enough information...
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Ah, now you tell me....

3x > 7 - 4y
x > (7 - 4y) / 3

or
4y > 7 -3x
y > (7 - 3x) / 4