Holt McDougal Algebra 1 5-5 Solving Linear Inequalities 5-5 Solving Linear Inequalities Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1
Dec 17, 2015
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities5-5 Solving Linear Inequalities
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Warm UpGraph each inequality.1. x > –5 2. y ≤ 0
3. Write –6x + 2y = –4 in slope-intercept form, and graph.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Graph and solve linear inequalities in two variables.
Objective
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
VOCABULARY
1. Linear inequality: similar to a linear equation, but the equal sign is replaced with an inequality symbol.
2. Solution of a linear inequality: any ordered pair that makes the inequality true.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Tell whether the ordered pair is a solution of the inequality.
Example 1A: Identifying Solutions of Inequalities
(–2, 4); y < 2x + 1
Substitute (–2, 4) for (x, y).
y < 2x + 1
4 2(–2) + 1
4 –4 + 14 –3<
(–2, 4) is not a solution.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Tell whether the ordered pair is a solution of the inequality.
Example 1B: Identifying Solutions of Inequalities
(3, 1); y > x – 4
Substitute (3, 1) for (x, y).
y > x − 4
1 3 – 4
1 – 1>
(3, 1) is a solution.
Holt McDougal Algebra 1
5-5 Solving Linear InequalitiesYou try!!!!
a. (4, 5); y < x + 1
Tell whether the ordered pair is a solution of the inequality.
b. (1, 1); y > x – 7
Holt McDougal Algebra 1
5-5 Solving Linear InequalitiesWhen the inequality is written as:
the points on the boundary line _________________of the inequality and the line is _____________
When the inequality is written as:
the points on the boundary line _________________of the inequality and the line is _____________
When the inequality is written as:
the points _______ the boundary line are _________________
When the inequality is written as:
the points _______ the boundary line are _________________
STEP 1 – HOW SHOULD I DRAW THE
BOUNDARY LINE?
STEP 2 – HOW SHOULD I SHADE?
𝒚 ≤𝒐𝒓 𝒚 ≥
are solutions
solid
𝒚<𝒐𝒓 𝒚>¿
are not solutions
dashed
𝒚>𝒐𝒓 𝒚 ≥ 𝒚<𝒐𝒓 𝒚 ≤above below
solutions of the inequality solutions of the inequality
Holt McDougal Algebra 1
5-5 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 McDougal Algebra 1
5-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
Example 2A: Graphing Linear Inequalities in Two Variables
y 2x – 3
Step 1 The inequality is already solved for y.
Step 2 Graph the boundary line y = 2x – 3. Use a solid line for .
Step 3 The inequality is , so shade below the line.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Example 2A Continued
Substitute (0, 0) for (x, y) because it is not on the boundary line.Check y 2x – 3
0 2(0) – 3
0 –3 A false statement means
that the half-plane containing (0, 0) should NOT be shaded. (0, 0) is not one of the solutions, so the graph is shaded correctly.
Graph the solutions of the linear inequality.
y 2x – 3
Holt McDougal Algebra 1
5-5 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 McDougal Algebra 1
5-5 Solving Linear Inequalities
Graph the solutions of the linear inequality.
Example 2B: Graphing Linear Inequalities in Two Variables
5x + 2y > –8
Step 1 Solve the inequality for y.
5x + 2y > –8 –5x –5x
2y > –5x – 8
y > x – 4
Step 2 Graph the boundary line Use a dashed line for >.
y = x – 4.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Step 3 The inequality is >, so shade above the line.
Example 2B Continued
Graph the solutions of the linear inequality.5x + 2y > –8
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Example 2B Continued
Substitute ( 0, 0) for (x, y) because it is not on the boundary line.
The point (0, 0) satisfies the inequality, so the graph is correctly shaded.
Check
y > x – 4
0 (0) – 4
0 –40 –4>
Graph the solutions of the linear inequality.5x + 2y > –8
Holt McDougal Algebra 1
5-5 Solving Linear InequalitiesTry on your own!!!
Graph the solutions of the linear inequality.
2x – y – 4 > 0
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads.
Example 3: Application
Write a linear inequality to describe the situation.
Let x represent the number of necklaces and y the number of bracelets.
Write an inequality. Use ≤ for “at most.”
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Example 3a Continued
Necklacebeads
braceletbeadsplus
is atmost
285beads.
40x + 15y ≤ 285
Solve the inequality for y.
40x + 15y ≤ 285–40x –40x
15y ≤ –40x + 285Subtract 40x from
both sides.
Divide both sides by 15.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Example 3b
b. Graph the solutions.
=
Step 1 Since Ada cannot make a
negative amount of jewelry, the
system is graphed only in
Quadrant I. Graph the boundary
line . Use a solid line
for ≤.
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
b. Graph the solutions.
Step 2 Shade below the line. Ada can only make whole numbers of jewelry. All points on or below the line with whole number coordinates are the different combinations of bracelets and necklaces that Ada can make.
Example 3b Continued
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
c. Give two combinations of necklaces and bracelets that Ada could make.
Example 3c
Two different combinations of jewelry that Ada could make with 285 beads could be 2 necklaces and 8 bracelets or 5 necklaces and 3 bracelets.
(2, 8)
(5, 3)
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Write an inequality to represent the graph.Example Together
y-intercept: 1; slope:
Write an equation in slope-intercept form.
The graph is shaded above a dashed boundary line.
Replace = with > to write the inequality
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
Try on your own!!!
Write an inequality to represent the graph.
y-intercept: slope:
Holt McDougal Algebra 1
5-5 Solving Linear Inequalities
HOMEWORK
PG. 364-366
#12-21, 30-40(evens), 41, 42