Which inequality represents the sentence? the difference of seven and two tenths and a number is more than twenty nine. (a.) 7.2 - n > 29 (b.) n - 7.2 greater than or equal to 29 (c.) 7.2 - n

The difference of seven and two tenths and a number is more than twenty nine.

7.2 -n >29

Choice A

answer A

Step-by-step explanation:

5 - 2x >= 1 × 7

5 - 2x >= 7

-2x >= 7 - 5

-2x >= 2

x

Option 2x +y is less than or equal to 3 and Y - X is greater than or equal to 2

Step-by-step explanation:

Locate on the graph a point that belongs to the region indicated, for example, the point (-3, 1)

Now we substitute this point in the inequalities and we test if it is satisfied. Let's try the second option.

We have:

So:

Both inequalities are satisfied. Therefore the correct option is option 2.

and

You can verify that by substituting this or some other point belonging to the region in the inequalities of the other options, these are not satisfied.

Option 2x +y is less than or equal to 3 and Y - X is greater than or equal to 2

Step-by-step explanation:

Locate on the graph a point that belongs to the region indicated, for example, the point (-3, 1)

Now we substitute this point in the inequalities and we test if it is satisfied. Let's try the second option.

We have:

So:

Both inequalities are satisfied. Therefore the correct option is option 2.

and

You can verify that by substituting this or some other point belonging to the region in the inequalities of the other options, these are not satisfied.

See attached diagram

Step-by-step explanation:

Graph the solution of the inequality First, draw the dotted line (dotted because the sign of the inequality is

Graph the solution of the inequality First, draw the solid line (solid because the sign of the inequality is ≥). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (blue part on the diagram).

The intersection of both regions is the solution of the system of two inequalities.

Step-by-step explanation:

12x+7

To solve

12x+7

Collect like terms

12x=-11-7

12x=-18

Divide through by 12

-18/12

=--3/2 or -1 1/2

5x-8 greater than 40

5x=40+8

5x=48

Divide through by 5

=48/5

9 3/5

Step-by-step explanation:

X has no value so there is no greater value

Then the system of inequalities that represents the graph is second option:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2

Step-by-step explanation:

The area shaded is below the blue line and above the red line.

1.) The blue line goes through the points:

P1=(0,3)=(x1,y1)→x1=0, y1=3

P2=(1,1)=(x2,y2)→x2=1, y2=1

Slope: m=(y2-y1)/(x2-x1)

m=(1-3)/(1-0)→m=(-2)/(1)→m=-2

Point-slope form:

y-y1=m(x-x1)

y-3=-2(x-0)→y-3=-2(x)→y-3=-2x→y-3+3=-2x+3→y=-2x+3

The area below the blue line is:

y

2x +y is less than or equal to 3

2.) The red line goes through the points:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(-2,0)=(x2,y2)→x2=-2, y2=0

Slope: m=(y2-y1)/(x2-x1)

m=(0-2)/(-2-0)→m=(-2)/(-2)→m=1

Point-slope form:

y-y1=m(x-x1)

y-2=1(x-0)→y-2=1(x)→y-2=x→y-2+2=x+2→y=x+2

The area above the red line is:

y>=x+2→y-x>=x+2-x→y-x>=2

y-x is greater than or equal to 2

Then the system of inequalities that represents the graph is:

2x +y is less than or equal to 3, and y-x is greater than or equal to 2