Question

Which of the following graphs shows the solution for the inequality y - 4 > 2(x + 2)?

Answer 1

D. Graph C

Explanation:

y - 4 > 2(x + 2)

y > 2x + 4 + 4

y > 2x + 8

Let y = 2x + 8, Then

X-intercept (0, 8)

Y-intercept (-4, 0)

Since the inequality sign is > we use broken line.

to test the direction, take (0, 0)

y > 2x + 8

0 > 0+ 8

0 > 8 Which is false

so, the answer will be above the broken line

Answer 2

D. Graph C

Explanation:

For many of these inequality graphing problems, you only need to consider two things:

• which side of the boundary line is shaded
• is the boundary line solid or dashed.

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You can pick any variable in the inequality that has a positive coefficient. Write that variable in the same relation with the inequality symbol that it has in the inequality. Here, that will be either of ...

• y >
• > x

These tell you the answers to both questions above.

line type

The inequality symbol does not include the "or equal to" (≥), so the boundary line is not part of the solution. The boundary line is dashed.

shading

The y values in the solution set are greater than those on the boundary line, so shading is above. The x-values in the solution set are less than those on the boundary line, so shading is to the left. (The boundary line has positive slope, so "above" and "left" are the same thing.)

The only graph with a dashed boundary line and shading above it is Graph C.