Day 3: Solving Inequalities with the Variable on Both Sides
Warm-Up
Model Problems
Solve. Express in set-builder notation and interval
notation. Graph each inequality.
1) 4m – 3 < 2m + 6
Set-builder Notation: _________________ Interval Notation: ______________
2) 2(k – 3) > 6 + 3k – 3
Set-builder Notation: _________________ Interval Notation: ______________
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Exercise
Solve for the value of the variable. Express as in inequality, setbuilder notation, and interval notation. Graph each inequality.
1) 4x ≥ 7x + 6
Set-builder Notation: __________________________________ Interval Notation: ______________
2) 5t + 1 < –2t – 6
Set-builder Notation: __________________________________ Interval Notation: ______________
3)
𝟗
𝟏𝟎
𝟒
𝟓
𝒚 ≥ 𝟏𝟎 𝒚 − 𝟏𝟎
Set-builder Notation: __________________________________ Interval Notation: ______________
4) 5(2 – r) ≥ 3(r – 2)
Set-builder Notation: __________________________________ Interval Notation: ______________
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5) − 35 < −3(3𝑛 + 3) + 1
Set-builder Notation: __________________________________ Interval Notation: ______________
𝟔)
𝟏
𝟑
𝟓
≤− 𝒎+𝟏+𝟏
𝟐
Set-builder Notation: __________________________________ Interval Notation: ______________
Identities and Contradictions
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Model Problems Solve for x. Tell the solution set.
𝑥+5 ≥𝑥+3
Exercise
2𝑥 + 6 ≤ 5 + 2𝑥
Solve for the value of each variable.
Lesson Summary


Solving a two-sided inequality is like solving an equation.
If the variable disappears, the result is an identity or a contradiction.
o If the resulting inequality is true, then it is an identity and the solution set is
all real numbers.
o If the resulting equation is false, then it is a contradiction and the solution
set is empty (no solutions).
o Examples:
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Homework
Solve for the value of the variable. Express in each notation shown.
Graph.
Inequality: ___________
Inequality: ___________
Set-builder: __________
Set-builder: __________
Interval: _____________
Interval: _____________
Inequality: ___________
Inequality: ___________
Set-builder: __________
Set-builder: __________
Interval: _____________
Interval: _____________
Inequality: ___________
Inequality: ___________
Set-builder: __________
Set-builder: __________
Interval: _____________
Interval: _____________
Inequality: ___________
Inequality: ___________
Set-builder: __________
Set-builder: __________
Interval: _____________
Interval: _____________
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Inequality: ___________
Inequality: ___________
Set-builder: __________
Set-builder: __________
Interval: _____________
Interval: _____________
Inequality:
___________
Inequality:
___________
Set-builder:
__________
Set-builder:
__________
Interval:
_____________
Interval:
_____________
Inequality:
___________
Set-builder:
__________
Interval:
_____________
Inequality:
___________
Set-builder:
__________
Interval:
_____________
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