6-5 Solving Linear Inequalities
Warm Up
Graph each inequality.
1. x > –5
3. Write –6x + 2y = –4
in slope-intercept form,
and graph.
y = 3x – 2
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2. y ≤ 0
6-5 Solving Linear Inequalities
Learning Target
Students will be able to: Graph and
solve linear inequalities in two
variables.
Holt Algebra 1
6-5 Solving Linear Inequalities
Tell whether the ordered pair is a solution of
the inequality.
(–2, 4); y < 2x + 1
y < 2x + 1
4
2(–2) + 1
4 –4 + 1
4 < –3 
(–2, 4) is not a solution.
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6-5 Solving Linear Inequalities
(3, 1); y > x – 4
y>x−4
1
3–4
1> –1

(3, 1) is a solution.
Holt Algebra 1
6-5 Solving Linear Inequalities
a. (4, 5); y < x + 1
b. (1, 1); y > x – 7
y<x+1
5
4+1
5 < 5
y>x–7
1
1–7
1 > –6 
(4, 5) is not a solution.
(1, 1) is a solution.
Holt Algebra 1
6-5 Solving Linear Inequalities
A linear inequality describes a region of a coordinate
plane called a half-plane. All points in the region are
solutions of the linear inequality. The boundary line of
the region is the graph of the related equation.
Holt Algebra 1
6-5 Solving Linear Inequalities
Holt Algebra 1
6-5 Solving Linear Inequalities
Graphing Linear Inequalities
Step 1
Solve the inequality for y (slopeintercept form).
Step 2
Graph the boundary line. Use a solid line
for ≤ or ≥. Use a dashed line for < or >.
Shade the half-plane above the line for y >
Step 3 or ≥. Shade the half-plane below the line
for y < or y ≤. Check your answer.
Holt Algebra 1
6-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
y  2x – 3
Check
y
0
2(0) – 3
0  –3 
 0, 0 
x
Holt Algebra 1
y  2x – 3
6-5 Solving Linear Inequalities
Helpful Hint
The point (0, 0) is a good test point to use if it
does not lie on the boundary line.
Holt Algebra 1
6-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
y
5x + 2y > –8
5x
2 y  5 x  8
2 2
2
5
Check y   x  4
2
5x
0
(0) – 4
0
–4
0 > –4
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 0, 0 
x
6-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
y
2x – y – 4 > 0
y
Check
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y
y  2x  4
0 2  0  4
04
0
4
 0, 0 
x
6-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
y
Check
y≥
0
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x+1
(0) + 1
0
0+1
0 ≥
1
 0, 0 
x
6-5 Solving Linear Inequalities
Ada has at most 285 beads to make jewelry. A
necklace requires 40 beads, and a bracelet
requires 15 beads.
 285
Let x represent the number of necklaces and y the
number of bracelets.
40 x  15 y  285
Holt Algebra 1
6-5 Solving Linear Inequalities
Remember, Ada can only use
whole numbers for x and y.
y
# of bracelets
40 x  15 y  285
40x
40x
15 y  40 x  285
15 15
15
8
y   x  19
3
In Algebra 2 we will determine
which of those points
maximizes profit!
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2
1
# of necklaces
x
6-5 Solving Linear Inequalities
Write an inequality to represent the graph.
3
y  x 1
4
y  mx  b
Holt Algebra 1
6-5 Solving Linear Inequalities
Write an inequality to represent the graph.
1
y
x 5
2
y  mx  b
HW pp. 418-420/12-21,30-42 Even,43-48,51-65
Holt Algebra 1