"First-degree Inequalities of One Variable" PPT Courseware 2

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"First-degree Inequalities of One Variable" PPT Courseware 2

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1. Properties of Inequalities

Properties of Inequalities 1: If the same number (or formula) is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.

Property 2 of inequalities: If both sides of the inequality are multiplied (or divided) by the same positive number, the direction of the inequality sign remains unchanged.

Property 3 of Inequality: When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes.

Note: You must change the direction of the inequality sign

Talk about it, draw a picture

Can x=5, 6, 8 make the inequality 2x+1>11 true?

Can you still find the value of x that makes the inequality 2x+1>11 hold?

Remember how to represent x>5 on the number line?

linear inequality of one variable

Both sides of the inequality are integers, contain only one unknown, and the highest degree of the unknown is 1. Such an inequality is called a linear inequality of one variable.

Solutions to linear inequalities of one variable

Solving linear inequalities of one variable is similar to solving linear equations of one variable, we have

Remove denominators, remove brackets, move items, merge similar items

The coefficients are reduced to 1 and other steps.

In the two steps of removing the denominator and reducing the coefficient to 1, special attention should be paid to when both sides of the inequality are multiplied (or divided) by a negative number, the direction of the inequality sign must change.

Example 3. Find the negative integer solution of inequality 3(1-x) ≤2(x+9).

Solution: Solve inequality 3(1-x) ≤2(x+9), and get x≥-3

Because x is a negative integer

So x=-3,-2,-1.

Find the positive integer solution of inequality 2(x-1)

show yourself

1. The solution set of inequality 2-x

2. When x=-3, 4x-3a>6, then the value range of a is _ _____.

3. When x______, the value of the algebraic formula -3x+12 is a non-negative number

4. Solve the inequalities and express the solution set on the number line.

(1) 2x-4>6x+2/2 (2) x-1/2(4x-1)<3/2

Classroom meets standards

1. If a>b, then which of the following inequalities is correct ( )

A. 4a<4b B.-4a<-4b C.a+4

2. The natural number solution of inequality 3 (x-1) ≥ 5x-3 is ______

3. When a______, the value of algebraic formula 2a-3 is not less than the value of 5a+3.

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Update Time: 2024-10-17

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