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MAT1033C Intermediate Algebra Lab 3: Basic Linear Inequalities

MAT1033C Intermediate Algebra
Lab 3: Basic Linear Inequalities Review
Lab Objectives:
1)
2)
3)
Solve One-Step Linear Inequalities in One Variable.
Solve Two-Step Linear Inequalities in One Variable.
Graph the Solution for a Linear Inequality in One Variable.
Directions: Complete the outline as you watch the video. Feel free to pause or rewind as needed.
Remember:
An interval is the solution set of an inequality if replacing the variable with any
number in the solution interval results in a true statement.
A linear inequality in one variable is written in the form Ax + B < C, Ax + B > C,
Ax + B ≀ C, or Ax + B β‰₯ C where A, B, and C are real numbers and A β‰  0.
Concept Check: Is 6 in the solution set of 3x + 4 < 15?
Replace x with 6.
3(6) + 4 = 18 + 4 = 22
22 is not < 13
Therefore 6 is NOT in the solution set of the inequality.
Objective 1: Solve One-Step Linear Inequalities in One Variable.
In order to solve linear inequalities we need to use INVERSE operations. The inverse of addition is
SUBTRACTION and the inverse of multiplication is DIVISION.
If the operations of addition or subtraction are applied to both sides of the inequality, the solution set
is not changed.
If the operations of multiplication or division by a positive number are applied to both sides of the
inequality, the solution set is not changed.
If the operations of multiplication or division by a negative number are applied to both sides of the
inequality, reverse the direction of the inequality sign.
The goal in solving a linear inequality is to have the variable on one side of the inequality sign and the
number on the other side. Once a solution is found, remember to check your answer by substituting a
number from the solution interval into the original inequality.
Examples: (Watch the video and work these with me.)
1. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 𝑑 βˆ’ 8 < 3
2. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 8 + 𝑀 > 14
3. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 3𝑛 ≀ 48
4. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 18 β‰₯
𝑐
2
5. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 11 ≀ 5 + π‘₯
6. π‘†π‘œπ‘™π‘£π‘’ π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: βˆ’ 168 ≀ βˆ’12π‘Ž
Objective 2: Solve Multi-Step Linear Equations in One Variable.
Sometimes it requires more than one step to solve an inequality.
Step 1:
Get the variable term on one side of the inequality and the number on the other.
Example: 3x β‰₯ 18
This may require adding or subtracting the same number to both sides of the
inequality. Use of the distributive property may also be required.
Step 2:
Solve for the variable. This may require multiplying or dividing both sides of the
inequality by the same number. Remember to reverse the direction of the inequality
sign if you multiply or divide by a negative number.
Step 3:
Check your answer by substituting a number in the solution interval in the original
inequality.
Examples: (Watch the video and work these with me).
π‘†π‘œπ‘™π‘£π‘’: 4𝑛 βˆ’ 7 > 16
4𝑛 > __________
𝑛>
23
_________
1. π‘†π‘œπ‘™π‘£π‘’: 4 + 2π‘₯ β‰₯ 24
Add 7 to both sides of the equation.
Divide each side by 4.
Yes, fractions can be part of the solution intervals.
2. π‘†π‘œπ‘™π‘£π‘’: 2𝑏 βˆ’ 3 < 5 βˆ’ 7𝑏
3. π‘†π‘œπ‘™π‘£π‘’:
π‘š
3
βˆ’ 3 ≀ βˆ’6
4. π‘†π‘œπ‘™π‘£π‘’: 4(π‘ž βˆ’ 6) β‰₯ 12
5. π‘†π‘œπ‘™π‘£π‘’: βˆ’ 4(3 + 𝑛) > βˆ’32
6. π‘†π‘œπ‘™π‘£π‘’: βˆ’ 7𝑦 + 7 ≀ βˆ’56
Objective 3: Graph the Solution for a One Variable Linear Inequality.
You can write the solution to an inequality using interval notation. Interval notation helps us
understand how to graph the solution for a one variable inequality on the number line.
𝑛>6
(6, ∞)
π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦ π‘›π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘›
π‘–π‘›π‘‘π‘’π‘Ÿπ‘£π‘Žπ‘™ π‘›π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘›
Examples: (Watch the video and work these with me).
1. πΊπ‘Ÿπ‘Žπ‘β„Ž π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 𝑑 < 11
2. πΊπ‘Ÿπ‘Žπ‘β„Ž π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 𝑀 > 12
3. πΊπ‘Ÿπ‘Žπ‘β„Ž π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: 𝑛 ≀ βˆ’4
4. πΊπ‘Ÿπ‘Žπ‘β„Ž π‘‘β„Žπ‘’ π‘–π‘›π‘’π‘žπ‘’π‘Žπ‘™π‘–π‘‘π‘¦: βˆ’ 1 ≀ 𝑐
Concept Check: Now you are prepared to answer the questions on the Lab 3 Worksheet. If you have
any difficulty, please take the Worksheet to the Math Lab along with your specific questions. The
Math Lab locations are listed below. The Math Lab website will post hours of operation for the current
semester: http://itech.pensacolastate.edu/mathlab/
Pensacola Campus – Building 1, Room 102, phone 484-2003
Warrington Campus – Building 3100, Room 3142D, phone 484-2378
Milton Campus – Building 4200, Room 4246, phone 484-4403 or 484-1041
South Santa Rosa Campus – Building 51, Room 5130A, phone 471-4630
Additional Resources:
http://www.kutasoftware.com/free.html - This site has plenty of algebra worksheets to use for practice.
We know you are not in the 8th grade, but this website has some tools that can help you improve your
algebra skills. Copy and paste this web address in your web browser and help is on the way!
http://www.ixl.com/math/grade-8
Check out the Algebra 1 tab (A1) to review all of your algebra skills!

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