Holt Algebra 1

6-5 Solving Linear Inequalities

Warm UpGraph each inequality.1. x > –5 2. y ≤ 0

3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2

Holt Algebra 1

6-5 Solving Linear Inequalities

Students will be able to: Graph and solve linear inequalities in two variables.

Learning Target

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 + 14 –3<

(–2, 4) is not a solution.

Holt Algebra 1

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

y < x + 1

b. (1, 1); y > x – 7

y > x – 7

5 4 + 15 5 <

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 (slope-intercept form).

Step 2Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.

Step 3Shade the half-plane above the line for y > 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

x

yCheck y 2x – 3

0 2(0) – 3

0 –3

0,0

Holt Algebra 1

6-5 Solving Linear Inequalities

The point (0, 0) is a good test point to use if it does not lie on the boundary line.

Helpful Hint

Holt Algebra 1

6-5 Solving Linear InequalitiesGraph the solutions of the linear inequality.5x + 2y > –8 5x 5x

2 5 8y x 2 2 2

54

2y x

x

y

0 (0) – 4

0 –40 –4>

Check

0,0

Holt Algebra 1

6-5 Solving Linear Inequalities

Graph the solutions of the linear inequality.

2x – y – 4 > 0 y y

2 4y x

x

y

0,0

Check

0 2 0 40 4

40

Holt Algebra 1

6-5 Solving Linear Inequalities

Graph the solutions of the linear inequality.

x

y

0,0

Check

y ≥ x + 1

0 (0) + 1

0 0 + 1

0 ≥ 1

Holt Algebra 1

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.

Write a linear inequality to describe the situation.

Let x represent the number of necklaces and y the number of bracelets.

285

40 15 285x y

Holt Algebra 1

6-5 Solving Linear Inequalities

819

3y x

15 40 285y x

40 15 285x y Solve for y and graph.

40x 40x

15 15 15

2

1 x

y

# of necklaces

# o

f bra

cele

ts

Remember, Ada can only usewhole numbers for x and y.

In Algebra 2 we will determinewhich of those pointsmaximizes profit!

Holt Algebra 1

6-5 Solving Linear Inequalities

Write an inequality to represent the graph.

y mx b

31

4y x

Holt Algebra 1

6-5 Solving Linear Inequalities

Write an inequality to represent the graph.

y mx b

15

2y x

HW pp. 418-420/12-21,30-42 Even,43-48,51-65