"From Calculation to Equation" PPT courseware for linear equations of one variable

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"From Calculation to Equation" PPT courseware for linear equations of one variable

Do you know what an equation is?

Equations with unknown numbers - Equations

Can you give some examples of equations?

practise:

1. Determine whether the following formula is an equation. Mark "√" if it is correct and "x" if it is incorrect.

(1) 1+2=3 ( ) (4) x + 2 ≥1 ( )

(2) 1+2x=4 ( ) (5)x+y=2 ( )

(3) x+1-3 ( ) (6)x2-1=0 ( )

Based on the following questions, assume the unknowns and list the equations:

Example 1: ① Use a 24cm long wire to form a rectangle so that its length is 1.5 times its width. What should be the length and width of the rectangle?

Solution: Assume the width of the rectangle is x cm, then the length is 1.5x cm.

The equation is: 2(x+1.5x)=24

②Girls account for 52% of all students in a school, 80 more than boys. How many students are there in this school?

Solution: Suppose there are x students in this school, then the number of girls is 0.52x and the number of boys is (1-0.52)x.

The equation is: 0.52x-(1-0.52)x=80.

③A computer has been used for 1,700 hours and is expected to be used for another 150 hours per month. How many months will it take for the computer to reach the prescribed maintenance time of 2,450 hours?

Assume that the usage time of this computer reaches 2 450 hours after x months, then it has been used for (1 700+150x) hours after x months.

The equation is: 1700+150x=2450.

Based on the following questions, assume the unknowns and list the equations:

(1) The circular track is 400m long. How many times can you run along the track for 3000m?

Solution: If you run x times along the track, you can run 3000m.

Make the equation: 400x=3000

(2) Pencils of type A cost 0.3 yuan each, and pencils of type B cost 0.6 yuan each. A total of 20 pencils of the two types were bought for 9 yuan. How many pencils of each type were bought?

Solution: Suppose y pencils of type A are bought, then (20-y) pencils of type B are bought.

The equation is: 0.3y+0.6(20-y)=9

(3) The lower base and upper base of a trapezoid are 2� more, the height is 5�, and the area is 40�2. What is the upper base?

Solution: Let the upper base be y�.

The equation is: (y+2+y) ×5÷2=40

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Update Time: 2024-10-07

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