Page 36 - Math Course 3 (Book 1)

Graphing Linear Inequalities

Write and Solve an Inequality

y
Example

y = 2x + 3 JOURNALISM
Lee Cooper writes and edits short articles for a
local newspaper. It takes her about an hour to write
an article and about a half-hour to edit an article. If
Lee works up to 8 hours a day, how many articles
0 x can she write and edit in one day?

Explore
You know how long it takes her to write and edit an
Step 3 article and how long she works each day.
Select a point in one of the half-planes and test it.
Let’s use (0, 0). Plan
Let x equal the number of articles Lee can write.
y > 2x +3 Original inequality Let y equal the number of articles that Lee can edit.
0 > 2(0) +3 x = 0, y = 0 Write an open sentence representing the situation.
0 > 3 false
number
of
Since the statement is false, the Number of 1 articles is
half-plane containing the origin articles she 2 she can up 8
Answer is not part of the solution. Shade can write plus hour times edit to hours.
the other half-plane. { { { { { { {
x + 1 • y < 8
2
y

Solve Solve for y in terms of x.

y = 2x + 3 1
x + y < 8 Original inequality
2

x + 1 y –x < –x + 8 Subtract x from each
2
0 x side.

1
y < –x + 8 Simplify.
2
1
Check (2) y < 2 (–x + 8) Multiply each side by 2.
2
Test a point in the other half-plane, for example,
(–3, 1). y < –2x + 16 Simplify.

y > 2x + 3 Original inequality
1 > 2(–3) + 3 x = –3, y = 1 Since the open sentence includes the equation,
1 > –3 graph y = –2x +16 as a solid line. Test a point in
one of the half-planes, for example, (0, 0). Shade
Since the statement is true, the half-plane the half-plane containing (0, 0) since 0 ≤ –2(0) + 16
containing (–3, 1) should be shaded. The graph is true.
of the solution is correct.

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