Looking for those formulas and methods about solving equations, solving linear and quadratic inequalities in one variable, and please adopt them.

The linear equation of one variable is very simple

Steps:

Remove brackets, move terms, merge, and reduce coefficients to 1

For example: 3x 7(x-1)=3 2(x 1)

Solution: Remove the brackets to get 3x 7x-7=3-2x 2

Move to get 3x 7x 2x=3 7 2

Combine similar terms: 12x=12

Change the coefficient to 1 to get x=1

Quadratic equation of one variable:

Only An integral equation that contains an unknown number and the highest degree of the unknown number is 2 is called a quadratic equation. The standard form of a quadratic equation is ax? bx c=0 (a, b, c are constants, x is an unknown number, and a≠0 ).

The steps for solving quadratic equations of one variable are generally: formula method, factoring method and matching method

Formula method:

First of all, the formula method is the discriminant △ (Greek letter, pronounced Delta) Relationship with 0

△>0 has two unequal real roots

△=0 has one real root

The △＜0 equation has no solution

For example, x? x 2=0

Then let’s look at △=b?-4ac

This Example a=1 b=1 c=2

Δ=1?-4×1×2 <0 So the equation has no solution

If it is x? x-2=0

a=1 b=1 c=-2

Then △=1?-4×1×-2 = 9>0

So the equation is The solution has two unequal real roots

They are (-b √△)/2a and (-b-√△)/2a

Next factoring method

There are no special requirements for factoring.

For example: 2x?-5x 2=0

We factorize: (2x-1)(x -2)=0, we will find x1=1/2, x2=2

Next, let’s talk about the matching method. The formula is all in the form of a completely flat formula (a±b)=a?±2ab b?.

We still use 2x?-5x 2=0 as an example

First, we change the coefficient to 1 and ÷2 on both sides at the same time to get x?-5/2x=-1

Next we add (5/4)? to both sides, and we get x?-5/2x (5/4)?=1 (5/4)?

(x-5/ 4)?=9/16

x-5/4=±3/4

So x1=1/2 x2= 2

The inequality problem is also It’s very simple and the same as the equation. See what else you don’t understand! 1