← Mathematics / 1 Numbers and Algebra
1.3 Linear Inequalities
Mathematics · Grade 11 · 8 lessons in the design
What this covers
- Simple and compound inequality statements in one unknown, on a number line
- Linear inequalities in two unknowns: boundary lines, solid or dashed
- Graphical solution of simultaneous linear inequalities, shading the unwanted region
- Forming simple linear inequalities from graphs; applications including speed limits and budgets
What you will be able to do
- solve compound inequalities in one unknown
- represent linear inequalities in two unknowns graphically
- solve linear inequalities in two unknowns graphically
- form simple linear inequalities from inequality graphs
- apply inequalities to real life situations
- appreciate the use of inequalities in real life
Key questions
“How are linear inequalities used in day to day life?”
Lessons
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Solving a simple inequality
40 min · 1 practice tasks · quizSolve a linear inequality in one unknown, reverse the sign when multiplying or dividing by a negative, and read a speed sign as an at-most statement.
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Compound inequalities
40 min · 1 practice tasks · quizSolve a three-part inequality, including one that reverses when the middle has a negative coefficient, and separate and from or.
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Whole-number solutions
40 min · 1 practice tasks · quizList the integers inside a solved compound inequality, and use a number line to keep the strict end out.
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The boundary line
40 min · 1 practice tasks · quizDraw the straight boundary of a linear inequality from its intercepts, and choose a solid or dashed line from the symbol.
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Shade the unwanted side
40 min · 1 practice tasks · quizTest one point, keep the side that satisfies the inequality clear, and shade the side that fails it.
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Two inequalities together
40 min · 1 practice tasks · quizFind the clear region that satisfies x at least 0, y at least 0, and x + 2y at most 6, and name its three corners.
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A region away from the origin
40 min · 1 practice tasks · quizSolve x at least 1, y at least 1, and x + y at most 5, name the three corners, and list the integer points inside.
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Reading an inequality from a region
40 min · 1 practice tasks · quizRecover the inequality from intercepts, a solid or dashed line, and which side is clear, then use the same idea for a budget.