8.9 多重不平等-interactive

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  多重不平等

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  Pet Iguana
  ::Iguana宠物

  

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  Jacob just bought a pet iguana and was told that a temperature below 75°F will be too cold for the lizard and a temperature above 95°F will be too hot.
  ::Jacob刚买了一只宠物蜥蜴 听说75°F以下的温度太冷了 蜥蜴太冷 95°F以上的温度太热了

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  Use the interactive below to determine which temperatures are safe for the lizard.
  ::使用下面的交互数据来确定蜥蜴的温度是安全的。

   

   

   

   

   

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  Compound Inequalities
  ::多重不平等

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  The scenario above represents a compound inequality , which is an inequality made using two or more simple inequalities.
  ::以上情况是一种复杂的不平等,是一种利用两种或两种以上简单的不平等造成的不平等。

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  One way to express the temperatures,  $\begin{align*}t,\end{align*}$  at which an iguana habitat must be kept  is:
  ::一种表示温度的方法, t, 即必须保持蜥蜴栖息地的温度,是:

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  $$\begin{align*}t ≥ 75 \text{ and } t ≤ 95\end{align*}$$
  ::t75和t95

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  T he  first inequality can be reversed without changing its meaning, resulting in $\begin{align*}75 ≤ t \text{ and }t ≤ 95.\end{align*}$  Then you can write the inequality more efficiently  by getting rid of the word “and” and combining the  $\begin{align*}t\text{'s:}\end{align*}$  

  $$\begin{align*}{75 \le t \le 95}\end{align*}$$
  ::第一个不平等可以在不改变其含义的情况下被扭转,从而导致 75 和 t95。 这样,你就可以通过消除“和”一词,把“和”合并起来,更有效地写出不平等。 75 和 95 。

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  The compound inequality  $\begin{align*}75 \le t \le 95\end{align*}$  means that  $\begin{align*}t\end{align*}$   must be greater than or equal to 75 and   less than or equal to 95 . In other words,  $\begin{align*}t \end{align*}$  is  between 75 and 95, inclusive ( inclusive means  the solution   includes   the endpoints of the inequality, 75 and 95). This all-in-one notation represents  the   range of numbers between  two values.
  ::75t95复合不平等意味着t必须大于或等于75,小于或等于95,换句话说,t在75至95之间,具有包容性(包容性意味着解决方案包括不平等的终点,即75和95)。

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  “And” inequalities represent scenarios where the solutions are values that satisfy both inequalities. These inequalities can be graphed similarly to simple inequalities, as shown below.
  ::“和”不平等是指解决方案是满足两种不平等的价值观的情景,这些不平等可与简单的不平等相似地加以描述,如下文所示。

  

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  Practice graphing compound “and” inequalities using the interactive below.
  ::使用以下互动方式绘制“和”不平等现象的做法图。

   

   

   

   

   

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  Sell or Stay?
  ::卖还是留下来?

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  Olivia is a stock trader: she buys and sells stocks. The goal of a stock trader is to buy a stock and sell it at a greater value. However, given the relatively unpredictable nature of the stock market, sometimes a stock will be sold at a value lower than the price at which it was purchased.
  ::Olivia是一个股票交易商:她买卖股票。 股票交易商的目标是购买股票并以更高的价值出售股票。 但是,鉴于股票市场相对不可预测,有时股票将以低于购买价格的价格出售。

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  Olivia just bought a stock for $150.32. She plans to sell the stock when its value is greater than or equal to $175. She will also sell the stock if the  value drops to less than or equal to $125.
  ::Olivia刚以150.32美元购买股票。当股票价值超过或等于175美元时,她打算出售股票。如果股票价值降到低于或等于125美元,她也将出售股票。

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  Use the interactive below to graph the compound “or” inequality that represents which values Olivia should sell her stock.
  ::利用下面的交互数据来绘制“或”不平等的化合物图,它代表着对Olivia的股票进行出售的价值。

   

   

   

   

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  The  stock trader scenario represents a compound inequality where the  solutions  are represented by values in opposite directions.
  ::股票贸易商的假想是一种复杂的不平等,其解决办法是以相反的价值观为代表的。

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  The compound inequality that represents the values at which Olivia  should sell the stock  is:
  ::代表Olivia出售股票价值的复合不平等是:

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  $$\begin{align*}t \le 125 \text{ or }t \ge 175\end{align*}$$
  ::t125或t175

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  Although this can be written as  $\begin{align*}125 \ge t \ge 175,\end{align*}$  this notation is  not generally used since it appears to suggest that $\begin{align*}t\end{align*}$  is between 125 and 175 when it is actually the opposite!
  ::虽然这可以写为125t175, 但通常不使用这个符号, 因为它似乎暗示t在125到175之间,

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  "Or"  inequalities  represent scenarios where the solutions are values that satisfy either inequality.  See the table below for additional examples.
  ::“或”不平等是指解决方案是满足其中任一不平等的价值观的情景。其他例子见下表。

  

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  Use the interactive below to practice graphing on a number line.
  ::在数字行上练习图形绘制。

   

   

   

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  Writing Multiple Inequalities
  ::写作多重不平等

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  Use the interactive below to practice writing compound inequalities for real world situations.
  ::在现实世界中,用下面的交互式文字来写出复杂的不平等。

   

   

   

   

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   Summary
  ::摘要

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  • Compound inequalities can be used to represent multiple inequalities.
    ::多重不平等可以用来代表多重不平等。
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  • "And" inequalities represent the values that satisfy both inequalities. For example, $\begin{align*}-3 < x < 1 \end{align*}$  means that $\begin{align*}x \end{align*}$  must be greater than -3 AND less than 1.
    ::“ 并且” 不平等代表满足两种不平等的价值观。 例如, 3 < x < 1 表示x必须大于 - 3 和小于 1 。
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  • "Or" inequalities represent the values that satisfy either inequalities. For example, $\begin{align*}x < -3 \text{ or } x > 1 \end{align*}$  means that $\begin{align*}x \end{align*}$  can be either  less  than -3 OR  greater  than 1.
    ::“ 或” 不平等代表满足不平等的价值观。 例如, x3 或 x>1 表示 x 可能小于 - 3 或大于 1 。