K_Algebra 1-2 Solving equations & inequalities (Round up or down, AND, Or)

About this unit

In this unit, we learn how to solve linear equations and inequalities that contain a single variable. For example, we'll solve equations like 2(x+3)=(4x-1)/2+7 and inequalities like 5x-2≥2(x-1).

 

Solving equations & inequalities (180/1100 Mastery points)

• Linear equations with variables on both sides
• Linear equations with parentheses
• Analyzing the number of solutions to linear equations
• Linear equations with unknown coefficients
• Multi-step inequalities
• Compound inequalities

--Analyzing the number of solutions to linear equations

从来没有想过用两条直线解决线性方程Linear equation。 0 = 0  or a = a， 是一条直线。 -22x -10 = -22x + 83  (two parallel  lines)是两条平行线, slopes in these two slopes are equals. 两条直线相交, -22x -10 = -21x + 83, in this situation, slope is not equal.

7x-10 -15x = -22x + 83 

-22x -10 = -22x + 83     (two parallel  lines)

-10 = 83  ( no solution)

--Multi-step inequalities

It is better to explain us rounding up or rounding down problems. The rule is not the pure mathematical rule on 5, it is based on situation shown in two examples here.

• #1 Roundup even decimal digit is less than 5. 

• #2 Round down even decimal digit is bigger than 5. 

--Compound inequalities

It is very interesting to see math education address compound inequalities in OR, AND, a set concept. One mistake I made is to change the direction of the comparative sign when calculate, for example, 12x > -36 becomes x < -3.