What is the inequality shown in the graph?

10x – y < 1
0.1x – y < 1
0.1x – y > 1
10x – y > 1

c. is the answer

  0.1x – y > 1

Step-by-step explanation:

The boundary line has a small positive slope (rise over run), so the inequality will be 0.1x + ... rather than 10x +

The graph is shaded to the right of the boundary line, so for x values greater than those on the line. That means the inequality is ...

  0.1x - y > 1 . . . . . . . . the form is ... x is greater than some value

If you like, you can restructure this inequality to the form ...

  y < 0.1x -1 . . . . . . slope-intercept form

so you can better see that the y-intercept is -1 (true for all of the choices) and the slope is 0.1. You can also see in this form that the shading will be for y-values below those on the boundary line.

Comment on shading direction

I find it easiest to find a variable in the equation that has a positive coefficient and look to see what the comparison operator is in relation to that:

 ( )x + ... > ...        will be shaded to the right of the line

 ( )x + ... < ...        will be shaded to the left of the line

 ( )y + ... > ...        will be shaded above the line

 ( )y + ... < ...        will be shaded below the line

When the inequality here is written in the slope-intercept form shown above, you can see that the shading will be below (y < ...) and to the right (x > ...) of the line. Since the line has positive slope, these descriptions of the shading both describe the same thing.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: