1.6 solving linear inequalities
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This document discusses solving linear inequalities. It defines inequality symbols and notes that a linear inequality involves one variable to the first power. It explains that a solution makes the inequality true. Transformations can be made to inequalities, such as adding/subtracting the same number or multiplying/dividing by a positive number, but multiplying/dividing by a negative number requires flipping the inequality sign. Graphing linear inequalities involves open or closed dots depending on the inequality sign. Compound inequalities joined by "and" or "or" can be solved by thinking of the solutions between or as oars on a boat.
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This document provides an overview of a lesson on solving and graphing inequalities. It includes student objectives like understanding properties of inequalities, solving singular and absolute value inequalities, and applying inequalities to real-life situations. Examples are provided to demonstrate solving different types of inequalities step-by-step and graphing the solutions. Students are asked to apply what they've learned to solve practice problems independently and discuss questions in pairs. The lesson aims to build students' skills in reasoning with inequalities.
Solving and graphing inequalities lecture 1
This document provides an overview of a lesson on solving and graphing inequalities. It includes student objectives like understanding properties of inequalities and learning how to solve singular and absolute value inequalities. Examples are provided to demonstrate solving different types of inequalities step-by-step and graphing the solutions. Real-world examples like parking restrictions are used to illustrate how inequalities apply in daily life. Formative assessments like a KWL chart and discussion questions are incorporated to check understanding.
119 Powerpoint 1.7
1. The document discusses linear inequalities in one variable, including interval notation versus inequality notation and solving single and double inequalities.
2. It provides examples of determining if a value is a solution to an inequality and discusses the rule that the sign of an inequality reverses if multiplying or dividing both sides by a negative constant.
3. An example problem solves the inequality 5x - 7 > 3x + 9, putting the solution in interval notation and graphing it on a number line. It also provides an example of solving a double inequality.
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This document discusses various methods for factoring trinomials of the form Ax^2 + Bx + C. It begins by outlining three main methods: trial and error, factoring by grouping, and the box method. It then provides examples of using the factoring by grouping method, demonstrating how to find two numbers whose product is AC and sum is B. The document also covers special cases like factoring the difference of squares using the form A^2 - B^2 = (A-B)(A+B), and factoring perfect square trinomials using the form A^2 + 2AB + B^2 = (A+B)^2. In all, it thoroughly explains the step-by
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Factoring GCF and Grouping
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This document discusses two special cases for multiplying binomials: difference of squares and perfect square trinomials. For difference of squares, multiplying (a + b)(a - b) results in a^2 - b^2. For perfect square trinomials, squaring a binomial (a + b)^2 follows the pattern of a^2 + 2ab + b^2. Some examples are worked out applying these rules.
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1.6 solving linear inequalities
- 2. Inequality SymbolsInequality Symbols ≠≥≤>< Less than Greater than Less than or equal to Greater than or equal to Not equal to
- 3. Linear Inequality • Inequality with one variable to the first power. for example: 2x-3<8 • A solution is a value of the variable that makes the inequality true. x could equal -3, 0, 1, etc.
- 4. Transformations for InequalitiesTransformations for Inequalities • Add/subtract the same number on each side of an inequality • Multiply/divide by the same positive number on each side of an inequality • If you multiply or divide by a negative number, you MUST flip the inequality sign!
- 5. Ex: Solve the inequality. 2x-3<8 +3 +3 2x<11 2 2 x< 2 11 1373 ≤+− x 63 ≤− x 2−≥x Flip the sign after dividing by the -3!
- 6. Graphing Linear Inequalities • Remember: < and > signs will have an open dot o and signs will have a closed dot graph of graph of ≤ ≥ 2 11 <x 2−≥x • 4 5 6 7 -3 -2 -1 0
- 7. Example: Solve and graph the solution. 121097 −≥+ xx 1239 −≥ x x321≥ x≥7 6 7 8 9
- 8. Compound Inequality • An inequality joined by “and” or “or”. Examples “and” “or” think between think oars on a boat 13 ≤<− x -4 -3 -2 -1 0 1 2 4or2 >−≤ xx -3 -2 -1 0 1 2 3 4 5
- 9. Example: Solve & graph. -9 < t+4 < 10 -13 < t < 6 Think between! -13 6
- 10. Last example! Solve & graph. -6x+9 < 3 or -3x-8 > 13 -6x < -6 -3x > 21 x > 1 or x < -7 Flip signs Think oars -7 1