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Authoritative PPT Summary
"Inequality" Equality and Inequality PPT (Solution Set of Inequality in Lesson 2)
Part One: Learning Objectives
Be able to solve linear inequalities of one variable and solution sets of groups of linear inequalities of one variable
Can solve the solution set of inequalities containing absolute values with the help of the geometric meaning of absolute values.
Inequality PPT, part 2 content: independent learning
Problem guide
Preview the contents of textbook P64-P67 and think about the following questions:
1. What is the solution set of an inequality?
2. What is the solution set of a system of inequalities?
3． What is the concept of absolute value inequality?
4. What is the geometric meaning of |a|?
5. If A and B are two different points on the number axis, what are the lengths of line segment AB and the midpoints of A and B respectively?
A preliminary exploration of new knowledge
1. Solution sets of inequalities and solutions of groups of inequalities
(1) Generally speaking, the set composed of ________ of inequalities is called the solution set of inequalities.
(2) For an inequality group obtained by combining several inequalities, the ______ of the solution set of these inequalities is called the solution set of the inequality group.
■Instructions from famous teachers
If the intersection of the solution sets of the inequalities contained in the inequality is ∅, then the solution set of the inequality group is ∅.
2. absolute value inequality
(1) The concept of absolute value inequality
Generally speaking, inequalities containing ____________ are called absolute value inequalities.
(2) The distance formula between two points on the number axis and the midpoint coordinate formula
Generally speaking, if the corresponding points of real numbers a and b on the number axis are A and B respectively, that is, A(a), B(b), then the length of line segment AB is |AB|=____________, line segment AB The number corresponding to the midpoint M is x = ____________.
■Instructions from famous teachers
(1) When finding the length |AB| of line segment AB, do not ignore the absolute value;
(2) The coordinates of the midpoint of line segment AB have nothing to do with the order of points A and B.
self-test
Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)
(1) The solution set of the inequality 2x+1>0 is -12, +∞.()
(2) The solution set of the inequality ax+b>0 is -ba, +∞.()
(3) The solution set of the inequality |x|<12 is -12, 12.()
(4) The solution set of the inequality |x|
(5) If |a|>|b|, then a>b.()
The solution set of the inequality group 2x-1>0, x+1<3 is ________.
The solution set of the inequality |x-1|<1 is ________.
The solution set of the inequality |x-2|>3 is ________.
If the coordinates of two points A and B on the number axis are A(2) and B(-4) respectively, then |AB|=________, and the coordinates of the midpoint M of line segment AB are _________.
Inequality PPT, the third part: interactive teaching and practice
Solutions to groups of inequalities
Solve the following set of inequalities:
(1)x-5>1+2x, ①3x+2≤4x; ②
(2)23x+5>1-x, ①x-1≤34x-18.②
regular method
Three Steps to Solving Systems of Inequalities
(1) Find the solution set of each inequality in the inequality group.
(2) Use the number line to find the common parts of each solution set.
(3) Write the solution set of the inequality group.
Solutions to Inequalities Containing an Absolute Sign
Solve the following inequalities:
(1)|2x+5|<7;
(2)|2x+5|>7+x;
(3)2≤|x－2|≤4.
regular method
Common types of inequalities with an absolute sign and their solutions
(1) Equivalence can be applied to inequalities of the form |f(x)|0) and |f(x)|>a(a>0) Use the transformation method to convert it into equivalent inequalities (sets) to solve.
(2) The solutions to inequalities of the form |f(x)|g(x) are as follows:
① Equivalent conversion method: |f(x)|＜g(x)⇔-g(x)＜f(x)＜g(x), |f(x)&# 124;＞g(x)⇔f(x)＜-g(x) or f(x)＞g(x)．
(Here g(x) can be positive or negative)
Solutions to Inequalities Containing Two Absolute Signs
Solve the following inequalities:
(1)|x-1|>|2x-3|;
(2)|x-1|+|x-2|>2;
(3)|x＋1|+|x＋2|＞3＋x.
regular method
(1) Solutions to absolute value inequalities |x|a
①|x|＜a⇔-a＜x＜a（a＞0），∅（a≤0）.
②|x|>a⇔x∈R (a<0), x∈R and x≠0 (a=0), x>a or x<-a (a>0).
(2) Solution of |ax＋b|≤c(c＞0) and |ax+b|≥c(c＞0) type inequalities
①|ax＋b|≤c⇔-c≤ax＋b≤c.
②|ax+b|≥c⇔ax+b≥c or ax+b≤-c.
(3) Solve |f(x)|>|g(x)| or |f(x)|<|g(x )| type inequality method is the square method, such as this example (1).
(4)|x-a|＋|x-b|≥c and |x-a|＋|x-b|≤c type inequality 2 solutions to
①Use the geometric meaning of absolute value inequality.
②Use the solution of x-a=0, x-b=0 to divide the number axis into three intervals, and then convert the original inequality into an inequality without absolute value in each interval and solve it.
Inequality PPT, Part 4: Feedback on Compliance
1. The solution set of the inequality group 2x-1≥5, 8-4x<0 is expressed as () on the number axis
2. The solution set of inequality 3≤|5-2x|<9 is ()
A． [－2,1)∪[4,7) B． (-2,1]∪(4,7]
C. [-2,1]∪[4,7) D． (-2,1]∪[4,7)
3． The solution set of the inequality |x-2|≤|x| is ________.
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