Download 1.5 Solving Inequalities_2

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?
Success Criteria:

I can identify inequality symbols

I can identify intersections of inequalities

I can solve compound inequalities
Today
1. Do Now
2. Check HW #5
4. Review Ch 1.2-1.5
5. HW #6
6. Complete iReady
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.
Example: Solving Inequalities
Solve and graph 8a –2 ≥ 13a + 8.
8a – 2 ≥ 13a + 8
–13a
–13a
–5a – 2 ≥ 8
+2
+2
–5a ≥ 10
–5a ≤ 10
–5
–5
a ≤ –2
•
–10 –9
–8 –7 –6 –5 –4
–3 –2 –1
Subtract 13a from both sides.
Add 2 to both sides.
Divide both sides by –5 and
reverse the inequality.
Check It Out! Example
Solve and graph x + 8 ≥ 4x + 17.
•
x + 8 ≥ 4x + 17
–x
–x
Subtract x from both sides.
8 ≥ 3x +17
–17
–17
Subtract 17 from both sides.
–6 –5
–4 –3 –2 –1
0
–9 ≥ 3x
–9 ≥ 3x
3
3
–3 ≥ x or x ≤ –3
Divide both sides by 3.
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.
6y < –24 OR y +5 ≥ 3
Solve both inequalities for y.
6y < –24
y + 5 ≥3
or
y < –4
y ≥ –2
The solution set is all points that satisfy
{y|y < –4 or y ≥ –2}.
–6 –5 –4 –3 –2 –1
0
1
2
3
Check It Out! Example 4
Solve the compound inequality. Then graph the
solution set.
–3x < –12 AND x + 4 ≤ 12
Solve both inequalities for x.
–3x < –12
and
x > –4
x + 4 ≤ 12
x≤8
The solution set is the set of points that satisfy both
{x|4 < x ≤ 8}.
2
3
4
5
6
7
8
9 10 11
Solve the compound inequality. Then graph the
solution set.
1. x – 5 < –2 OR –2x ≤ –10
–3 –2 –1
0
1
2
3
8
9 10 11
4. –3x < –12 AND x + 4 ≤ 12
2
3
4
5
6
7
4
5
6
HW #6
Pg 38 # 12-42 x 3 and 51
Example 1: Solving Compound Inequalities
Solve the compound inequality. Then
graph the solution set.
x – 5 < –2 OR –2x ≤ –10
Solve both inequalities for x.
x – 5 < –2
or
–2x ≤ –10
x<3
x≥5
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
Check It Out! Example 3
Solve the compound inequality. Then graph the
solution set.
2x ≥ –6 AND –x > –4
Solve both inequalities for x.
2x ≥ –6
and
–x > –4
x ≥ –3
x<4
The solution set is the set of points that satisfy both
{x|–3 < x < 4}.
–4 –3 –2 –1 0
1
2
3
4
5
Lesson Quiz: Part I
Solve. Then graph the solution.
1. y – 4 ≤ –6 or 2y >8
–4 –3 –2 –1 0
{y|y ≤ –2 ≤ or y > 4}
1
2
3
4
5
2. –7x < 21 and x + 7 ≤ 6 {x|–3 < x ≤ –1}
–4 –3 –2
–1 0
1
2
3
4
5
Solve each equation.
3. |2v + 5| = 9
2 or –7
4. |5b| – 7 = 13
+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
Solve.
1. 2(3x – 1) = 34
x=6
2. 4y – 9 – 6y = 2(y + 5) – 3
y = –4
3. r + 8 – 5r = 2(4 – 2r)
4. –4(2m + 7) =
all real numbers, or

(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 Up
Solve.
1. y + 7 < –11
y < –18
2. 4m ≥ –12
m ≥ –3
3. 5 – 2x ≤ 17
x ≥ –6
Use interval notation to indicate the graphed
numbers.
4.
(-2, 3]
5.
(-, 1]