8.7 不平等解决方案-interactive

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  不平等解决方案

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  Measuring Profit
  ::衡量利润

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  E very business uses the same basic equation to calculate how much money it makes : Revenue – Expenses = Profit. Revenue is the amount of money brought in by sales and profit is  the money left over after paying for expenses .
  ::每个企业都使用相同的基本方程式来计算它赚了多少钱:收入 — — 支出 — — 利润。 收入是销售带来的钱,利润是支付费用后留下的钱。

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  Example
  ::示例示例示例示例

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  Jenny owns a bakery and  expects to have $450,000 in expenses this year. If she hopes to earn $370,000 in profit , h ow much revenue will she need to achieve her goal?
  ::Jenny拥有一家面包店,预计今年会有45万美元的开支。 如果她希望赚取37万美元利润,那么她需要多少收入来实现她的目标?

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  Given her expenses, use the interactive below to figure out how much revenue Jenny needs to make to earn a profit.
  ::鉴于她的费用,请使用下面的交互数据来计算珍妮为了赚取利润需要挣多少收入。

   

  

  INTERACTIVE

  Measuring Profit

  

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  • Use the slider to change the value of the Revenue.
    ::使用滑块更改收入的值。
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  • Observe how this changes Profit on the number line.
    ::观察这如何改变数字行上的利润 。

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  According to the number line, which of the following results in a negative profit?
  ::根据数字线,以下哪些结果为负利润?

  a 播放段落

  Profit > Revenue
  ::利润 > 收入

  b 播放段落

  Revenue < Expenses
  ::收入 <支出 >

  c 播放段落

  Profit < Revenue
  ::利润 < 收入

  d 播放段落

  Revenue > Expenses
  ::收入 >支出

   

   

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  Identifying Inequality Solutions
  ::查明不平等解决方案

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  You  know that to determine if a number is a solution to an equation,  you can substitute the value of the variable with the number and determine if the statement is true.  You  can take the same approach with answers that are in the solution set of  an inequality .
  ::您知道, 要确定一个数字是否是一个方程的解决方案, 您可以用数字来替代变量的值, 并且确定该语句是否真实 。 您可以采取同样的做法, 回答是不平等的解决方案 。

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  Example
  ::示例示例示例示例

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  Is 10 a solution for  $\begin{array}{r}a>13?\end{array}$
  ::10是解决a>13的解决方案吗?

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  S ubstituting 10 for  $\begin{array}{r}a,\end{array}$  you get $\begin{array}{r}10>13.\end{array}$  This statement is not true.
  ::以 10 代替 a, 你得到 10 > 13 。 这个声明不正确 。

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  Look at the inequality  $\begin{array}{r}a>13\end{array}$  plotted below.  Notice that the number 10 is not in the highlighted section of numbers.
  ::请注意,十位数不在数字的突出部分。

  

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  Answer: No, the number 10 is not a solution to the inequality  $\begin{array}{r}a>13.\end{array}$
  ::答复:否,第10号不是解决不平等问题的办法a。

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  Use the interactive below to practice identifying whether a given number is a solution to the inequality.
  ::利用以下互动方式确定某一数字是否是解决不平等问题的办法。

   

  

  INTERACTIVE

  Identifying Inequality Solutions

  

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  • Check the box for whether or not the given number is a solution to the inequality.
    ::检查框中是否给定数字是不平等的解决办法。
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  • Check your answer with the "Check" button.
    ::用“ 检查” 按钮检查您的回答 。
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  • Press "Next" to try a new problem.
    ::按下“ 下一步” 来尝试一个新问题 。

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  One-Step Inequalities
  ::单位不平等

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  Just as  you   can solve  a one-step equation for the specific value that makes the equation true, you can solve one-step inequalities for  the set of values that make the statement of inequality true.
  ::正如你能够解决一个使方程式真实的具体价值的单步方程一样,你也可以解决使不平等声明真实的一套价值的单步不平等。

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  Example
  ::示例示例示例示例

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  Is 6 a solution to the inequality  $\begin{array}{r}12+a\le 20?\end{array}$
  ::6是解决12+a20不平等的解决方案吗?

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  This  inequality  asks the question, “When added to 12, what values are  less  than or equal to 20?" U se the same approach  you did in the previous activity: substitute the variable with the number and determine if the statement is true.
  ::这种不平等提出一个问题,“如果加上12,什么值小于或等于20?” 使用与您在前一次活动中同样的做法:用数字替代变量,并确定声明是否真实。

  $$\begin{array}{rl}12+6& \le 20\\ 18& \le 20\end{array}$$

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  Answer: Yes, 6 is a solution to the inequality  $\begin{array}{r}12+a\le 20,\end{array}$  because  $\begin{array}{r}12+6=18,\end{array}$  which is less than 20.
  ::回答:是的,6是解决12+a20不平等的一个办法,因为12+6=18,低于20。

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  In the interactive below, find a range of values for $\begin{array}{r}a\end{array}$  that satisfies the inequality.
  ::在下文互动中,找到满足不平等的一系列价值观。

   

  

  INTERACTIVE

  One-Step Inequalities

  

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  • Identify the range of values that are a solution to the given equation.
    ::确定解决给定方程式的数值范围。
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  • Drag the red dots to change the lowest and highest values of the range.
    ::拖曳红色点以更改范围中最小和最高值。
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  • Check your answer with the button.
    ::用按钮检查您的回答 。

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  播放段落

  Use the interactive below to practice identifying whether a given number is a solution to the inequality.
  ::利用以下互动方式确定某一数字是否是解决不平等问题的办法。

   

  

  INTERACTIVE

  Identifying One-Step Inequality Solutions

  

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  • Check the box for whether or not the given number is a solution to the one-step inequality.
    ::检查框中是否给定数字是单步不平等的解决办法。
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  • Check your answer with the "Check" button.
    ::用“ 检查” 按钮检查您的回答 。
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  • Press "Next" to try a new problem.
    ::按下“ 下一步” 来尝试一个新问题 。

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  Measuring Profit Continued
  ::衡量利润持续计量

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  At the beginning of this lesson, you found the revenue that would result in a goal profit. However, this only represents the minimum amount of revenue needed to reach the goal.
  ::开始这个教训的时候,你发现了能带来目标利润的收入。然而,这只是达到目标所需的最低收入数额。

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  How does this change your answer?
  ::这如何改变你的答案?

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  Example
  ::示例示例示例示例

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  Jenny owns a bakery and plans to have $450,000 in expenses this year. If she hopes to earn at least $370,000 in profit, how much revenue will she need to achieve her goal?
  ::珍妮拥有一家面包店,并计划今年有450,000美元的开支。 如果她希望至少赚取370,000美元的利润,那么要实现她的目标,她需要多少收入?

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  This problem is an example of a one-step inequality. The goal is for revenue minus expenses to be greater than or equal to the desired profit.
  ::这个问题是一等不平等的一个例子,目标是使收入减去支出大于或等于预期利润。

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  •  Revenue:  $\begin{array}{r}x\end{array}$
  ::• 收入:x

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  •  Expenses: $450,000
  ::• 支出:450 000美元

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  •  Profit: $370,000
  ::• 利润:370 000美元

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  The inequality statement is  $\begin{array}{r}x-450,000\ge 370,000.\end{array}$
  ::不平等情况说明为x-450,000-370,000。

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  Solving  a one-step inequality is  similar to   solving a one-step equation . The difference is that your  solution will represent a range of  value rather than a single value .
  ::解决一步骤不平等与解决一步骤等式相似。 区别在于你的解决方案将代表一系列价值,而不是单一价值。

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  $$\begin{array}{rl}x-\cancel{450,000}& \ge 370,000\\ +\cancel{450,000}& +450,000\\ x& \ge 820,000\end{array}$$

  
  ::370,000+450,000+450,000x820,000

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  This means that values of $\begin{array}{r}x\end{array}$   greater than or equal to 820,000 make the inequality true.
  ::这意味着x大于或等于82万的值使不平等成为事实。

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  Answer: Jenny will need revenue of $820,000 or more to achieve her goal profit.
  ::回答:珍妮需要820,000美元或更多收入来实现她的目标利润。

   

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  Forklift Conundrum
  ::叉车难题

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  A forklift  has a maximum lift weight of 3,300 lbs and  needs  to be used to transport bags of cement across a construction site. Each cement bag weighs 75 lbs.
  ::叉车最大升降重量为3 300磅,需要用于在建筑工地上运输水泥袋,每个水泥袋重75磅。

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  In the interactive below, add transport bags of cement to the forklift in order to make an inequality modeling the maximum amount of bags the forklift can carry.
  ::在下文互动部分,在叉车上添加水泥运输袋,以便形成一种不平等模式,将叉车所能携带的袋子的最大数量作为模型。

   

  

  INTERACTIVE

  Forklift Conundrum

  

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  Drag the slider to change the number of cement bags on the forklift.
  ::拖动滑块以改变叉车上的水泥袋数量。

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   Summary
  ::摘要

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  • A  value is a solution to an inequality if substituting  the value into the variable  results in a true statement.
    ::如果用真实的报表将价值替换成变量结果,那么价值就是不平等的解决办法。
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  • To solve a one-step inequality, use inverse operations to get the variable by itself.
    ::为了解决一步步的不平等, 使用反向操作来获得变量本身 。
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  • The solution to an inequality is a range of values. 
    ::解决不平等问题是一系列价值观。