1. Derivation process
Move the term "ax+b=c" to get "ax=c-b", and then divide both sides of the formula by a to get x = (c-b)/a.
2. Practical application
One-dimensional linear equation is widely used to solve various practical problems in life, such as calculating the discount price of goods and calculating the investment income.
3. Handling of special circumstances-denominator is zero
If a=0, the equation degenerates to "bx=c". At this time, when b=0, no matter what value C takes, there are countless solutions. When b is not equal to 0, there is a unique solution if and only if c/b = x.
4. Handling of Special Cases-Molecular Zero
If c-b=0, the equation degenerates to "ax=0". At this time, when a=0, no matter what value X takes, there are countless solutions. When a is not equal to 0, x=0 is the only solution.
5. On the solution of one-dimensional linear equations
For the equations with two or more linear equations, we can use the elimination method to solve the unknown quantity, thus completing the solution of the equations.
6. Deformation solution of one-dimensional linear equation
When the equation can't be solved directly by the solving formula, the deformation method can be used to simplify the problem. For example, for the equation "2x-3=7x+5", you can first move the variable terms on both sides of the equation to the same side and the constant terms to the other side:
2x-7x=5+3
-5x=8
x=-8/5
7. Image of one-dimensional linear equation
One-dimensional linear equation can be regarded as a straight line equation, its image is a straight line in two-dimensional coordinate system, its slope k is the coefficient a of X in the equation, and its intercept b is a constant term in the equation. The solution of the equation is the abscissa of the intersection of the straight line and the X axis, that is, the intersection of the straight line on the image.
8. Examples of practical applications
Suppose a merchant carries out promotional activities, and the discounted price of a commodity with the original price of X yuan is Y yuan. It is known that the original price of a commodity is 20 yuan, and the price is 9 yuan after 4.5% discount. What is the discount for this promotion?
If the discount intensity is d, there is: 20*( 1-d)=9. The value of d can be obtained by deformation:
d= 1-9/20=0.55
That's 55% discount.
9. Summary
One-dimensional linear equation is one of the most basic contents in mathematics, and mastering its solution can provide an important guarantee for solving practical problems. Whether it is the need of study or the practical application in life, linear equation is a mathematical knowledge point that everyone needs to master skillfully.