Understand the equation 02: 10.
Numbers and Algebra in Junior Middle School Mathematics —— One-dimensional Linear Equation 12: 14
One-dimensional linear equation with parameter 03: 12
Solving linear equation of one variable (2) 02: 16
Video explanation of integer problem solving 02:56
One-dimensional linear equation
Popular Science China | This entry is reviewed by the entry writing and application project of Popular Science China.
Judge Shang Yilun
One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions. A linear equation with one variable has only one root. One-dimensional linear equation can solve most engineering problems, travel problems, distribution problems, profit and loss problem, integral table problems, telephone billing problems and digital problems. [ 1]
One-dimensional linear equations first appeared in ancient Egypt about 1600 BC [1]. Around 820 AD, the mathematician Hua La Zi Mi put forward the idea of "merging items" and "shifting items" in his book "Eliminating Yuan and Reducing Yuan". /kloc-in the 6th century, after the mathematician David founded symbolic algebra, he put forward the proposition of shifting terms and dividing by the same equation [2]. 1859, mathematician Li officially translated this kind of equation into one-dimensional linear equation [1].
Chinese name
One-dimensional linear equation
Foreign name
One-dimensional linear equation
Standard notation
Ax+b=0 or ax=b(a≠0)
type
Integral equation, linear equation
founder
Vedas
correlated curriculum
Junior high school mathematics unary linear equation series courses
To learn
quick
navigate by water/air
Research on the application value and significance of concept definition root-seeking method
trace the history (of)
One-dimensional linear equations were first seen in ancient Egypt around 1600 BC. [ 1]
About BC 1650, the 24th question was recorded in rhind papyrus scroll of ancient Egypt, and the title was: "A quantity, plus its.
Equal to 19, find this quantity. "solved the shape.
First-order equation, that is, a single hypothetical method to solve the problem.
Hua rami zi
Around 1 century BC, China people first added negative numbers to the arithmetic of nine chapters, put forward the arithmetic of positive and negative numbers, and solved the problem of shifting terms. In the chapter of "insufficient profit", the skills of insufficient profit are put forward. However, this method has not been used to solve one-dimensional linear equations. 1 1 to1was introduced into Arabia in the 3rd century, which was called "Khitan algorithm".
In the 9th century A.D., the Arab mathematician Hua Lazimi gave simple and feasible basic methods to understand equations, namely "reduction" and "elimination". But no alphabetic symbols are used. It embodies the obvious idea of the equation.
/kloc-In the 20th century, the Indian mathematician Bashgaro solved a class of linear equations by assuming (setting unknowns). Since the assumed number can be any positive number, Pashgaro calls the above method "any number algorithm".
/kloc-in the 3rd century, China's complementary technique was introduced to Europe, and the Italian mathematician Fibonacci used single hypothesis and double hypothesis to solve linear equations in his book Calculation.
Vedas
/kloc-in the 6th century, after David founded symbolic algebra, he put forward such propositions as shifting term and equation division, and also created this concept, which was honored as "the father of modern mathematics". But Vida doesn't accept negative numbers.
/kloc-in the 6th century, Cheng Dawei (1533- 1606), a mathematician in the Ming dynasty, also used the hypothesis method to solve a linear equation.
1859, Chinese mathematician Li officially translated this kind of equations into linear equations. [ 1]
Concept definition
There is only one unknown, the higher order of the unknown is 1, and both sides of the equal sign are algebraic expressions. Such an equation is called a linear equation with one variable. [1] Its general form is:
Sometimes writing:
Integral equation (e.g.
) is also a linear equation. One-dimensional linear equations are linear equations with only one root.
Root seeking method
conventional process
There are five steps to solve a linear equation with one variable, namely, denominating, removing brackets, shifting terms, merging similar terms, and the transformation coefficient is 1. All steps are carried out according to the properties of algebraic expressions and equations. [ 1]
To solve this equation
For example:
If you remove the denominator, you will get:
Without parentheses, you get:
To move an item, you must:
Merge similar items, get: (usually abbreviated as "merge, get:")
The coefficient becomes 1, and we get:
In one-dimensional linear equations, the denominator removal step is usually multiplied by the least common multiple of each denominator. If the denominator is a fraction, it can be replaced by the other part of the item multiplied by the reciprocal of the fraction on the denominator. [2]
equation
For example:
Eliminating the fraction on the denominator can be simplified as:
Then find the solution of the equation.
If there is an irrational number on the denominator, it is necessary to make the denominator rational first.
Root formula method
basic recipe
about
One-dimensional linear equation
, the root formula is:
deductive procedure
Solution: Move the term and get:
The coefficient becomes 1, and we get:
method of images
about
One-dimensional linear equation
You can do a function once
To solve it. One-dimensional linear equation
The root of is its corresponding linear function.
When the function value is 0, the independent variable
The value. That is, the abscissa of the intersection of the linear function image and the x axis. [3]
linear function
equation
For example:
As shown, make a function.
Image of.
From the image, we know that the function image intersects the X axis at a point.
The root of the original equation is
Research and application
basic application
One-dimensional linear equations can usually be used to do mathematical application problems, and [1] can also be used to calculate physics and chemistry.
For example, in production and life, by knowing a certain liquid density and pressure, by
The depth of liquid can be calculated by substituting the formula into the solution equation. For example, to calculate how high the atmospheric pressure is, it is known that the atmospheric pressure is about 100000 Pascal, the density of water is about 1000 kg per cubic meter, and g is about 10 m per square second (10 cattle per kg), then the water column height can be set to h m, and the square Cheng Kewei/kloc.