"Solving linear equations of one variable" PPT courseware 2

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"Solving linear equations of one variable" PPT courseware 2

The ancient Greek mathematician Diophantus (around 250 BC) is known as the father of algebra. Little is known about his life story, but his works are included in a book called "Selected Greek Poetry". epitaph:

"Diophantus is buried in the tomb. How amazing it is, how faithfully it records the path it has taken. The childhood given by God is one-sixth, and after another one-twelfth, beards grow on the cheeks, and after seven One-third, the wedding candles were lit. Five years later, God bestowed a son. Poor late Ning Xiner, half the age of his father, entered the cold tomb. The sorrow could only be made up for by the study of number theory. After another four years, He has also completed the journey of life.”

Question 1: Do you know how many years Diophantus lived?

Question 2: If Diophantus lived x years, what kind of equation can you formulate based on the description on the epitaph?

How to remove the denominator:

First find the least common multiple of several denominators, and then according to the second property of the equation, multiply both sides of the equation by the least common multiple to eliminate the denominator.

How to remove the denominator:

① Find the least common multiple of the denominator

②Multiply this common multiple by the terms on the left and right sides of the equation

Organize knowledge points:

The steps to solve a linear equation of one variable are:

(1) Remove the denominator.

(2) Remove the brackets.

(3) Move items.

(4) Combine similar items

(5) Divide both sides of the equation by the coefficient in front of the unknown.

Ability and improvement

Solve the equation: 4(x-1)+6(3-4x)=7(4x-3)

How many different solutions do you have? Which solution do you think is easier?

Fill in the spaces below with the same appropriate number to make the equation true:

12×46□=□64×21 (46□ and □64 are both three-digit numbers)

analyze:

If the number in the box is x, how should the equation be listed like this?

12×(460+x)=(100x+64)×21

Solving this equation, we get x=2

Finally, the results obtained should be tested.

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Update Time: 2024-07-06

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