"Basic Properties of Equations" PPT Courseware 4

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"Basic Properties of Equations" PPT Courseware 4

Determine which of the following expressions are equations and which are not equations?

①4+x=7, ② 2x, ③3x+1,

④a+b=b+a, ⑤ c=2πr ,⑥1+2=3,

⑦ab, ⑧ S=ah, ⑨2x-3y

Equality property 1:

Add (or subtract) the same number (or formula) to both sides of the equation, the result is still an equation

If a=b, then a±c=b±c

Notice

1. Both sides of the equation must participate in operations, and they must perform the same operation.

2. The numbers added or subtracted on both sides of the equation must be the same number or the same formula.

Equality property 2:

Multiply (or divide) both sides of the equation by the same number or formula (the divisor is not 0),

The result is still the equation

If a=b, then ac=bc or a/c=b/c

Notice

1. Both sides of the equation must participate in operations, and they must perform the same operation.

2. The numbers multiplied or divided by on both sides of the equation must be the same number or the same formula.

1. Based on the conditions of each of the following questions, write an equation that still holds true.

(1)a=-b, add b to both sides

(2)3a=2a+1, subtract a from both sides

(3)a/3=b/4-1, multiply both sides by 12

(4)a+1/x=1, multiply both sides by x

2. (1) If x+3=1, according to property 1 of the equation, subtract x from both sides of the equation at the same time.

Then 3=1-x.

(2) If x+3=1, according to the property 2 of the equation, multiply both sides of the equation by -2.

Then -2(x+3)=-2,

(3) If x+3=1, according to the property 1 of the equation, subtract 3 from both sides of the equation.

Then x=1-3,

(4) If x+3=1, then x+3/3, according to the property 2 of the equation, divide by 3 or multiply on both sides of the equation.

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Update Time: 2024-11-03

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