摘要:一个变量的线性等同和不平等

In this chapter, we learned about :
::在本章中,我们了解到:

Solving Linear Equations of One Variable or Literal Equations
::一种变量或公升等量的溶解线性线性等量

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• First, use the distributive property.    
  ::首先,使用分配财产。
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• Second, combine like terms on the same side of the equation.    
  ::第二,将方程的同一侧的类似条件结合起来。
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• Third, combine like terms on opposite sides of the equation.    
  ::第三,在等式的对面结合类似条件。
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• Fourth, perform addition or subtraction on both sides of the equation.    
  ::第四,在等式两侧增减。
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• Fifth, perform multiplication or division on both sides of the equation.    
  ::第五,在等式两侧进行乘法或分法。
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• Lastly, check your answer by substituting your solution back into the original equation.
  ::最后,检查一下你的答案 换回原来的方程
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• If the equation is in the form of a fraction equal to a number, multiply both sides by the denominator first.
  ::如果方程的形式是分数等于数,则双方首先乘以分母。

Solving Linear Inequalities of One Variable
::解决一个变量的线性不平等

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• Follow the same steps as for linear equations with one exception :
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  • If you multiply or divide both sides of the inequality by a negative number, you need to switch the direction of the inequality.
    ::如果您将不平等的两边乘以负数,或者将不平等的两边除以负数,您需要改变不平等的方向。
  
  ::遵循线性方程式的相同步骤,只有一个例外:如果将不平等的两边乘以负数或以负数分隔,则需要改变不平等的方向。

Solving Compound Inequalities of the Form,  $\begin{array}{r}a<x<b\end{array}$  (or  $\begin{array}{r}\le \end{array}$  )
::解决表单 <x <b (或___)的复合物不平等

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• Either separate the two inequalities and solve separately, 
  ::将两种不平等分开,分别解决,
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• Or make sure to perform any operations on all three expressions in the inequality.
  ::或者确保对不平等的所有三个表达式进行操作。

Solving Absolute Value Equations
::解决绝对值

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• Absolute value is the distance from 0 on the number line.
  ::绝对值是数字线上 0 的距离。
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• The distance between two numbers on the number line is $\begin{array}{r}|b-a|\end{array}$ .
  ::数字线上两个数字之间的距离是 b-a 。
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• To solve equations, remove the absolute value bars and consider a positive possibility (counting units to the right) and a negative possibility (counting units to the left).
  ::解决方程式,删除绝对值条,考虑积极的可能性(向右计数单位)和消极的可能性(向左计数单位)。

Solving Absolute Value Inequalities
::解决绝对价值不平等

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• You can solve absolute value inequalities graphically or algebraically.
  ::您可以用图形或代数来解析绝对值不平等。
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• To solve absolute value inequalities algebraically, consider two possibilities—one where you remove the absolute value bars and the other where you remove the absolute value bars, switch the direction of the inequality, and negate the number.
  ::解决绝对值不平等的代数,考虑两种可能性——一种是删除绝对值条,另一种是删除绝对值条,改变不平等的方向,否定数字。
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• Less than inequalities have solutions of AND-type compound inequalities and greater than inequalities have solutions of OR-type compound inequalities.
  ::不平等程度低于不平等可解决的化合物不平等问题,而不平等程度大于不平等可解决的或类型化合物不平等问题。

Translating Verbal Statements to Algebraic Statements
::将口头发言译成代数发言

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• Identify the unknown in the expression or statement by assigning it a variable.
  ::指定一个变量来识别表达式或语句中的未知值。
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• Look for key words in the verbal statements to translate into algebra.
  ::寻找口头发言中的关键词,将其翻译成代数。

Looking Back, Looking Forward
::回顾,展望未来

In this chapter, we considered equations and inequalities in which a variable is compared to a fixed amount. For example, we determined the number of hours worked given a fixed salary or the amount of soda that could be in a bottle given a fixed amount of error when it was filled. But what happens when these fixed amounts vary? That is what we will discuss in the next chapter.
::在本章中,我们考虑了一个变量与固定金额比较的方程式和不平等。例如,我们确定了给定工资的工时数,或者瓶中可能装的苏打水的工时数,在装满时给定差数。但是,当这些固定金额变化时,会发生什么情况?这就是我们将在下一章中讨论的内容。

Chapter Review
::回顾章次审查