Algebra 1 · Chapter 3 of 16

Inequalities & Absolute Value

Greater/less-than problems and absolute-value equations

Solve, graph, and model inequalities and absolute value relationships.

Common CoreA-REI.B.3A-CED.A.1

6 lessons21 short videos5 key concepts, out loud

3.1
Multi-Step Inequalities (The Flip Rule)
Solve inequalities and learn when to flip the sign
A-REI.B.3
Key idea
Solve inequalities using standard equation-solving steps, but flip the inequality sign whenever you multiply or divide both sides by a negative number.
Learn to solve multi-step inequalities, graph their solutions, and master the negative flip rule.
Key concept · Lesson 3.1
Flip only for a negative divide
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Transcript. Solve an inequality exactly like an equation. Undo addition, then undo multiplication. Only one move is different: when you multiply or divide both sides by a negative number, turn the inequality sign around. Adding or subtracting a negative never flips it.
3.2
Compound Inequalities (And vs. Or)
Solve and graph double inequalities using 'and' or 'or'
A-REI.B.3
Key idea
'And' inequalities require both conditions to be true (overlapping region), while 'or' inequalities require at least one to be true (combined regions).
Learn to solve compound inequalities and graph their solutions as overlapping or split intervals on a number line.
Key concept · Lesson 3.2
And overlaps; or keeps either one
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Transcript. A compound inequality joins two conditions. An and statement needs both to be true at once, so shade only where the two graphs overlap. An or statement needs just one, so keep both regions. Test a sample point whenever the shading is unclear.
3.3
Absolute Value Equations
Solve equations with absolute value by splitting them into two cases
A-REI.B.3
Key idea
To solve an absolute value equation, first isolate the absolute value expression, then split it into two separate equations: one positive and one negative.
Learn how to isolate an absolute value expression and split it into two separate equations to find all possible solutions.
Key concept · Lesson 3.3
Isolate, then split into two
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Transcript. Absolute value measures distance, so it is never negative. Get the bars alone on one side before you do anything else. Then split into two equations, one with the positive result and one with the negative result. If the isolated bars equal a negative number, there is no solution.
3.4
Absolute Value Inequalities
Solve absolute value inequalities using 'and' or 'or'
A-REI.B.3
Key idea
Rewrite 'less-than' absolute value inequalities as 'and' compound inequalities, and 'greater-than' as 'or' compound inequalities.
Learn how to rewrite absolute value inequalities as compound inequalities to solve and graph them.
Key concept · Lesson 3.4
Less than means and; greater than means or
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Transcript. Isolate the bars first. A less-than inequality traps the expression between two numbers, so write an and statement and shade the middle. A greater-than inequality pushes it outward, so write an or statement and shade both ends. Remember to flip the sign in the negative case.
3.5
Modeling with Inequalities
Write inequalities to solve real-world problems
A-CED.A.1
Key idea
Translate constraint words like 'at least' or 'no more than' into inequality symbols to model real-world limits.
Translate real-world limits and budget constraints into inequalities and solve them.
Key concept · Lesson 3.5
Translate the limit words
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Transcript. Real problems hide the symbol inside a phrase. At least and at most both include the boundary value, so they use the sign with a line underneath. More than and fewer than exclude it. Name your variable, write the limit, then solve the inequality as usual.
3.6
Review & Assessment
Inequalities and absolute value, mixed
Review, practice, quiz and test
Key idea
Review inequalities and absolute value with targeted mixed practice, a practice test, and a chapter test.