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Solving Linear Inequalities Solve:
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Linear Inequalities in One Variable
Objective: To solve linear inequalities
Interval notation
• We can express our answers in two ways. We can use the inequality signs ( < or > ) or we can use interval notation.
xx
xx
20353
),(]2,0[),3(
]5,3(
Solving Linear Inequalities
• Solve: 9375 xx
Solving Linear Inequalities
• Solve:• Add 7• Subt 3x• Divide by 2 or
8162
16359375
xx
xxxx
),8(
Solving Linear Inequalities
• You try: 14264 xx
Solving Linear Inequalities
• You try:
]10,(10202202414264
xx
xxxx
Solving Linear Inequalities
• Solve: 4231 xx
Solving Linear Inequalities• Solve:
• Mult by 2• Subt 2• Subt 2x• Divide by -5• When you multiply or divide by a negative number
you must change the inequality sign.
]2,(210510238232
4231
orxx
xxxx
xx
Solving Linear Inequalities
• You try: 95113 xx
Solving Linear Inequalities
• You try:
),10(
102022053
95113
orxxxx
xx
Solving a Double Inequality
• Solve: 3163 x
Solving a Double Inequality
• Solve:
• We need x by itself. Whatever we do to one term, we do to all three.
3163 x
Solving a Double Inequality
• Solve:
• We need x by itself. Whatever we do to one term, we do to all three.
• Add 1• Divide by 6 or
3163 x
32
31
4623163
x
xx
)3/2,3/1[
Solving a Double Inequality
• You try: 206212 x
Solving a Double Inequality
• You try:
]7,3(
731426
206212
orxxx
Solving an Absolute Value Inequality
• Solve: 2|5| x
Solving an Absolute Value Inequality
• Solve:
• We want to be closer than 2 units from zero. We need to look at 2 and -2.
------|---------|----------|------- -2 0 2
2|5| x
|5| x
Solving an Absolute Value Inequality
• Solve:
• We want to be closer than 2 units from zero. We need to look at 2 and -2.
------|---------|----------|------- -2 0 2
2|5| x
|5| x
25 x25 x
Solving an Absolute Value Inequality
• Solve:
and
2|5| x
725
xx
325
xx
)7,3(
Solving an Absolute Value Inequality
• Solve: 7|3| x
Solving an Absolute Value Inequality
• Solve:
• We now want values 7 units or more away from zero.
7|3| x
Solving an Absolute Value Inequality
• Solve:
• We now want values 7 units or more away from zero.
--------|--------------|---------------|------- -7 0 7
7|3| x
73x73 x
Solving an Absolute Value Inequality
• Solve:
or
7|3| x
),4[473
xx
]10,(1073
xx
Solving an Absolute Value Inequality
• You Try:
10|53| x 3|72| x
Solving an Absolute Value Inequality
• You Try:
and or
10|53| x 3|72| x
51531053
xxx
3/5531053
xxx
242372
xxx
5102372
xxx
Homework
• Pages 150-151• 19-29 odd• 37,39• 45-53 odd
