"Basic Properties of Equations" PPT Courseware 7

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"Basic Properties of Equations" PPT Courseware 7

①4+x=7, ② 2x, ③ 3x+1,

④a+b=b+a, ⑤ a2+b2 ⑥ c=2πr

⑦ 1+2=3, ⑧ 2/3ab, ⑨S=1/2ah,

⑩ 2x-3y>0

In the above set of formulas, (①④⑥⑦⑨) is an equation, and (②③⑤⑧⑩) is not an equation. Why?

Judgment based on the equation 1+2=3:

1+2+4＝3+4

1+2-5＝3-5

What properties do the above two questions reflect about the equation?

If you add (or subtract) the same number to both sides of an equation, the result is still an equation.

Judgment based on the equation 2x+3x=5x:

2x+3x+4x＝5x+4x

2x+3x-x＝5x-x

What properties do the above two questions reflect about the equation?

If you add (or subtract) the same equation to both sides of the equation, the result is still an equation.

answer:

(1) Can we get x+5=y+5 from x=y? Why?

(2) Can we get x/9=y/9 from x=y? Why?

(3) Can we get a=b from a+2=b+2? Why?

(4) Can we get a=b from 3a=3b? Why?

Know it

By deforming the equation step by step through operations, and finally changing it into the form of "x=a (a is a known number)", the value of the unknown is found, that is, the solution of the equation is found. The basis for the deformation is the two properties of the equation.

Knowledge sorting

△Two basic properties of the equation:

⒈If the same number or formula is added to or subtracted from both sides of the equation, the result is still an equation.

⒉If both sides of the equation are multiplied or divided by the same non-zero number or formula, the result is still an equation.

△Using the basic properties of the equation to transform the equation into the form of "x=a" is to solve the equation (that is, to find the solution of the equation).

Determine whether the following calculation process is correct:

Transform the equation x2=2x

Solution: According to property 2 of the equation, divide both sides by x, we get

x2/x＝2x/x

So x=2

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Update Time: 2024-11-17

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