理解线性等式

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Using Equations in Business
::商业中使用等同

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In this section, you'll be taking a deeper look into equations. In ,  you learned that an equation is a statement that two expressions are equal. This equality is shown using the equal symbol. The equal symbol tells us that the value of the expression on the left side of the symbol is the same as the value of the expression on the right. This  property of equations allows  you to find the value of a variable if all other quantities are known. A linear equation is an equation where each term has an exponent of 1. You will be working exclusively with linear equations in this lesson. 
::在本节中, 您将会对方程式进行更深的查看。 在 中, 您会了解到方程式是一个两个表达式相等的语句。 此等等式会使用相同的符号显示。 等式会告诉我们符号左侧表达式的值与右边表达式的值相同。 此等式的属性允许您在所有其他数量都已知的情况下找到变量的值。 线性方程式是一个公式, 每个术语的外号为 1 。 您将在本课中专门使用线性方程式 。

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Consider this example of how equations are used in business:
::考虑一下在商业中如何使用方程式的这个例子:

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The profit of a company is determined using the equation $\begin{array}{r}\text{Profit}=\text{Total Revenue - Total Cost}.\end{array}$  Christie McDonogh owns a small business called Christie’s Cookie Company. Last year, she earned a profit of $2 7 ,000 and had a total cost of $156,000. She is moving to a new location and expects her total costs to increase to $183 ,000. What would her total revenue have to be to earn the same profit?
::公司利润是根据利润=总收入-总成本等式确定的,Christie McDonogh拥有一家名为Christie的Cookie公司(Christie Cookie Company)的小企业。 去年,她赚取了27 000美元的利润,总成本为156 000美元。 她正在搬到一个新地点,预计总成本将增加到183 000美元。 她的总收入要赚取同样的利润又是什么?

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Discussion Question
::讨论问题

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What equation could you use to find the total revenue?
::你能用什么方程式来找到总收入?

 

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Finding A Solution
::寻找解决方案

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The equation from the example involving Christie’s Cookie Company is $\begin{array}{r}27,000=R-183,000.\end{array}$  Take a moment to consider what the solution to this problem means. A solution is a value for the variable which makes both sides of the equation equal.  You are looking for the value of $\begin{array}{r}R\end{array}$ :  the number that results in 27,000 when 183,000 is subtracted from it . Remembering that an equation is a statement that two expressions are equal; the two expressions are 27,000 and  $\begin{array}{r}R-183,000\end{array}$ .  You need a value of  $\begin{array}{r}R\end{array}$  that will make both sides of the equation equal. Since the left side is the constant 27,000, you need a value of $\begin{array}{r}R\end{array}$  that makes the right side of the equation equal to 27,000.
::Christie Cookie Cookie 公司的例子中的方程式是 27 000= R-183 000。 花一点时间来考虑这个问题的解决方案意味着什么。 解决方案是使方程式两侧均等的变量值。 您正在寻找 R 值 : 当从中减去 183 000 时, 得出的数值为 27 000 。 记住一个方程式是两个表达式相等的语句; 两个表达式是 27 000 和 R-183 000 。 您需要 R 值, 使方程式两侧均等。 由于左侧是常数 27 000, 您需要 R 值, 使方程式右侧等于 27 000 。

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Use the interactive below to determine which value of $\begin{array}{r}R\end{array}$  makes the right side of the equation equal to 27,000.
::使用下面的交互作用来确定 R 的哪个值使方程右侧等于 27 000 。

 

 

 

 

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In the interactive above, you found the value of $\begin{array}{r}R\end{array}$  which resulted in both sides having a value of 27,000.
::在上述互动中,你发现了R的价值,导致双方的价值为27 000美元。

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This means that the value of $\begin{array}{r}R\end{array}$  which made both sides of the equation equal to 27,000, is the solution to the equation.
::这意味着使等式两边均等于27 000的R值是等式的解决办法。

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Use the interactive below to practice finding the value that makes each of the equations true.
::使用下面的交互方式来练习找到使每个方程式都真实的价值。

 

 

 

 

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Discussion Question
::讨论问题

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In this case, you were able to substitute and test values to determine whether a potential solution made the equation true or false. What do you think some of the difficulties of this strategy might be?
::在这种情况下,你能够替代和测试价值来确定一个潜在解决方案是否使方程式成为真实或虚假。 你认为这一策略的某些困难是什么?

 

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Testing for Validity
::有效性测试

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When a value makes both sides of the equation equal to the same number, we say that the equation is true. When a value makes  each side of  an equation equal to a different number, we say that the equation is false.
::当一个值使方程的两面等于相同数字时,我们说方程是真实的。当一个值使方程的两面等于不同数字时,我们说方程是虚假的。

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Use the interactive questions below to practice determin ing whether potential solutions make  an equation true or false.
::利用以下交互式问题来实际确定潜在解决办法是否使等式成为真实或虚假。

 

 

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Discussion Question
::讨论问题

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Geneva claims that since substitution isn’t the best approach to solving an equation, it isn't important to learn it. Do you agree or disagree? State why you think it is or isn't important to know how to do substitution?
::日内瓦宣称,由于替代不是解决方程式的最佳方法,学习它并不重要。 你是否同意或不同意? 国家为什么认为知道如何进行替代不重要?