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5.5 Notes Alg1.notebook January 08, 2013
Skills we've learned
Skills we need
5.5 Solving Linear Inequalities
Solve all three ways:1) 2)y = x + 5
y = 2x + 4 y + x = 8x 8 = y–
Graph:3) y < 3 4) y ≥ 5
Warmup AnswersSolve all three ways:1) 2)y = x + 5
y = 2x + 4 y + x = 8x 8 = y–
Graph:3) y < 3 4) y ≥ 5
5.5 Notes Alg1.notebook January 08, 2013
5.5 Solving Linear Inequalities
Check solutions to an inequalityGraph and solve linear inequalities in two variables
Consumers can use linear inequalities to determine how much food they can buy for an event.
(–2, 4) is not a solution
I. Identifying Solutions of InequalitiesTell whether the ordered pair is a solution of the inequality.
1. (–2, 4); y < 2x + 1
Substitute (–2, 4) for (x, y).
2. (3, 1); y > x – 4
(3, 1) is a solution.
Substitute (3, 1) for (x, y).
5.5 Notes Alg1.notebook January 08, 2013
II. Graphing Linear Inequalities
A linear inequality describes a region of a coordinate plane called a halfplane. All points in the region are solutions of the linear inequality. The boundary line of the region is the graph of the related equation.
boundary line
halfplane
II. Graphing Linear Inequalities
Step 3: Test a point NOT on the line.
Step 1: Graph the line like normal.
Step 2: Graph with solid or dashed line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 4: If true, shade the side with the point. If false, shade the other side.
5.5 Notes Alg1.notebook January 08, 2013
II. Graphing Linear Inequalities
Graph the solutions of the linear inequality.
3. y ≤ 2x – 3
Substitute (0, 0) for (x, y) because it is not on the boundary line. A false statement means that the halfplane containing (0, 0) should NOT be shaded. (0, 0) is not one of the solutions, so the graph is shaded correctly.
hint
Step 3: Test a point NOT on the line.
Step 1: Graph the line like normal.Step 2: Graph with solid or dashed line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 4: If true, shade the side with the point. If false, shade the other side.
Graph the solutions of the linear inequality.
4. 4x – y + 2 ≤ 0
Step 3: Test a point NOT on the line.
Step 1: Graph the line like normal.Step 2: Graph with solid or dashed line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 4: If true, shade the side with the point. If false, shade the other side.
5.5 Notes Alg1.notebook January 08, 2013
5. Graph the solutions of the linear inequality.
A) 4x – 3y > 12
B) 2x – y – 4 > 0
Step 3: Test a point NOT on the line.
Step 1: Graph the line like normal.Step 2: Graph with solid or dashed line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 4: If true, shade the side with the point. If false, shade the other side.
Special!6. Graph x > 4 on a coordinate plane.
What about y ≤ 8?
5.5 Notes Alg1.notebook January 08, 2013
IV. Writing an Inequality from a Graph
7. Write an equation in slopeintercept form.
The graph is shaded above a dashed boundary line.
Replace = with > to write the inequality:
A) B) 8.
5.5 Notes Alg1.notebook January 08, 2013
III. Application
9. Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads.
a. Write a linear inequality to describe the situation.
Let x represent number of necklaces and y the number of bracelets.Write an inequality. Use ≤ for “at most.”
40x + 15y ≤ 285
b. Graph the inequality. Solve for y or find intercepts and graph the boundary line first. Since Ada cannot make a negative amount of jewelry, the system is graphed only in Quadrant I. Finally, shade.
All points whole number coordinates in the shaded area are the different combinations of bracelets and necklaces that Ada can make.
c. Give two combinations of necklaces and bracelets that Ada could make.
What do these ordered pairs mean in the context of the problem?(2,8) or (5,3)
5.5 p.364 #3 11, 13, 17 21, 27 30
After Final Exam Review Chapter 1, please also do Chapter 1 Study Guide p.84 #5, 12, 20, 21, 24, 35, 36, 39, 46, 49, 53, 56, 65
Both Due Thursday!5.4
5.5Review Ch. 1
5.6 Review Ch. 2
Review Ch. 5
Review Ch. 5 and Ch. 3 & 4
Test Ch. 5Final Exam Review
No school
Review for Final
5.5 Notes Alg1.notebook January 08, 2013
1) 15 = x – 2 2) 34.5 = y + 2.6 3) 108 = 9x
4) x = 160 5) = – 4 6) 7x + 5 = 26
7) The two triangles are similar. Find the length of x.
58
x9
3m
2m
x
4.4m
8) 5n + 45 – 12n = 66 9) –10x + 23 + 12x + 23 = 4
10) y + 20 = 0 11) 2x + 12 – 5x = 9 – (6x + 3) 311
Previous Review For Chapter 1 Answers Already Posted
12) One cab company charges $6 to pick you up and $4.50 each mile thereafter. Another charges no pick up fee, but charges $6 per mile. At how many miles is the first company more economical?
13) Write 7y – 2x = 7 as a function of x. (solve for y)
14) Sally Snow skied for 45 minutes and fell 135 times. How many times did she fall per minute?
15) Ratio of frogs to lily pads is 2:3, if there are 51 lily pads, how many frogs?
16) 2 |x + 5| = 8 17) 4|x| = 28 18) 19) 20) solve for b
Previous Review For Chapter 1 Answers Already Posted
