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Success Criteria:I can identify inequality symbolsI can identify intersections of inequalitiesI can solve compound inequalities
Today1. Do Now 2.Check HW #54.Review Ch 1.2-1.55.HW #66.Complete iReady
Do Now (Turn on laptop to my calendar)1. Write the equation and solve. Lisa and Beth have babysitting jobs. Lisa earns $30 per week and
Beth earns $25 per week. How many weeks will it take for them to earn a total of $275? How much more money does Lisa have?
An inequality is a statement that compares two expressions by using the symbols <, >, ≤, ≥, or ≠.
The graph of an inequality is the solution set, the set of all points on the number line that satisfy the inequality.
The properties of equality are true for inequalities, with one important difference.
If you multiply or divide both sides by a negative number, you must reverse the inequality symbol.
Solve and graph 8a –2 ≥ 13a + 8.
Example: Solving Inequalities
Subtract 13a from both sides.
8a – 2 ≥ 13a + 8
–13a –13a
–5a – 2 ≥ 8Add 2 to both sides. +2 +2
–5a ≥ 10Divide both sides by –5 and reverse the inequality.
–5 –5
–5a ≤ 10
a ≤ –2
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
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Solve and graph x + 8 ≥ 4x + 17.
Subtract x from both sides.
x + 8 ≥ 4x + 17
–x –x
8 ≥ 3x +17Subtract 17 from both sides.–17 –17
–9 ≥ 3x
Divide both sides by 3.
3 3
–9 ≥ 3x
–3 ≥ x or x ≤ –3
Check It Out! Example
–6 –5 –4 –3 –2 –1 0 1 2 3
•
A compound statement that uses the word and.
‘And’ Statement: x ≥ –3 AND x < 2
And statement is true if and only if all of its parts are true. And statements can be written as a single statement as shown.
x ≥ –3 and x< 2 –3 ≤ x < 2
A compound statement is made up of more than one equation or inequality.
OR statement: x ≤ –3 OR x > 2
An ‘or’ statement is true if and only if at least one of its parts is true.
Example 1A: Solving Compound Inequalities
Solve the compound inequality. Then graph the solution set.
Solve both inequalities for y.
The solution set is all points that satisfy {y|y < –4 or y ≥ –2}.
6y < –24 OR y +5 ≥ 3
6y < –24 y + 5 ≥3
y < –4 y ≥ –2or
–6 –5 –4 –3 –2 –1 0 1 2 3
Solve both inequalities for x.
–3x < –12 and x + 4 ≤ 12
2 3 4 5 6 7 8 9 10 11
–3x < –12 AND x + 4 ≤ 12
x > –4 x ≤ 8
The solution set is the set of points that satisfy both {x|4 < x ≤ 8}.
Solve the compound inequality. Then graph the solution set.
Check It Out! Example 4
Solve the compound inequality. Then graph the solution set.
x – 5 < –2 OR –2x ≤ –10
–3x < –12 AND x + 4 ≤ 12
1.
4.
–3 –2 –1 0 1 2 3 4 5 6
2 3 4 5 6 7 8 9 10 11
HW #6
Pg 38 # 12-42 x 3 and 51
Example 1: Solving Compound Inequalities
Solve the compound inequality. Then graph the solution set.
Solve both inequalities for x.
The solution set is the set of all points that satisfy {x|x < 3 or x ≥ 5}.
–3 –2 –1 0 1 2 3 4 5 6
x – 5 < –2 OR –2x ≤ –10
x < 3 x ≥ 5
x – 5 < –2 or –2x ≤ –10
Solve both inequalities for x.
2x ≥ –6 and –x > –4
–4 –3 –2 –1 0 1 2 3 4 5
2x ≥ –6 AND –x > –4
x ≥ –3 x < 4
The solution set is the set of points that satisfy both {x|–3 < x < 4}.
Solve the compound inequality. Then graph the solution set.
Check It Out! Example 3
Lesson Quiz: Part I
Solve. Then graph the solution.
1.
2.
y – 4 ≤ –6 or 2y >8
–7x < 21 and x + 7 ≤ 6
{y|y ≤ –2 ≤ or y > 4}
{x|–3 < x ≤ –1}
–4 –3 –2 –1 0 1 2 3 4 5
–4 –3 –2 –1 0 1 2 3 4 5
Solve each equation.
3. |2v + 5| = 9 4. |5b| – 7 = 13
2 or –7 + 4
Lesson Quiz: Part I
1. Alex pays $19.99 for cable service each month.
He also pays $2.50 for each movie he orders
through the cable company’s pay-per-view
service. If his bill last month was $32.49, how
many movies did Alex order?
5 movies
Do Now – use computer to identify learning target
y = –4
x = 6
all real numbers, or
Solve.
1. 2(3x – 1) = 34
2. 4y – 9 – 6y = 2(y + 5) – 3
3. r + 8 – 5r = 2(4 – 2r)
4. –4(2m + 7) = (6 – 16m) no solution, or
Lesson Quiz: Part III
5. Solve and graph.
12 + 3q > 9q – 18 q < 5
–2 –1 0 1 2 3 4 5 6 7
°
Warm UpSolve.1. y + 7 < –11
2. 4m ≥ –12
3. 5 – 2x ≤ 17
y < –18
m ≥ –3
x ≥ –6
Use interval notation to indicate the graphed numbers.
4.
5.
(-2, 3]
(-, 1]
