3.7 解决双层两层-interactive

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  解决双层平方

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  In This Lesson
  ::在本课程中

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  You will  learn to solve  two -step equations.  In order to get the variable by itself, or isolate it, you need to undo the operations that are on the same side of the equation as the variable.  However, if you do something to one side of an equation, you must do it to the other side too . Equations are like balances, and if you only undo an operation on one side, it becomes unbalanced and untrue. 
  ::您将学会解析两步方程。 为了自己获得变量, 或孤立它, 您需要撤销与变量相同方程的一边操作。 但是, 如果您对方程的一边做点什么, 您也必须对另一方做点什么。 等式和平衡相似, 如果您只撤销一边的操作, 它就会变得不平衡和不真实 。

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  For example , if the variable is getting multiplied by 3, you would need to divide by 3 to get the variable by itself . To  keep the equation balanced, though, you must divide by 3  on both sides .
  ::例如,如果变量乘以 3 , 您需要除以 3 才能将变量本身除以 3 。 但是, 要保持方程平衡, 您必须在两边除以 3 。

   

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  Balancing Equations
  ::平衡平等

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  In this interactive, y our goal is to keep the equation balanced while solving for $\begin{array}{r}x.\end{array}$  Each arm of the balance represents each side of the equation.
  ::在此互动中,您的目标是平衡方程式,同时解决 x 。 平衡的每个手臂代表方程式的两侧 。

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  The interactive will tell you if it is not balanced and when the equation is solved correctly. Click on the buttons at the top of the interactive to add and subtract ones and $\begin{array}{r}x\text{'s.}\end{array}$  In the end, division buttons will appear, so that you can isolate $\begin{array}{r}x.\end{array}$
  ::互动将会告诉您它是否平衡, 当方程式解答正确时 。 单击互动方程式顶部的按钮添加并减去那些和 x。 最终, 将出现分割按钮, 这样您就可以分离 x 。

   

  

  INTERACTIVE

  Balancing Equations

  

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  • Add or subtract the correct values on both sides of the equation to take out the constant on the left of the equation while keeping the equation balanced.
    ::添加或减去方程式两侧的正确值,以除去方程式左侧的常数,同时保持方程式平衡。
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  • Then, divide both sides by the correct value to take out the coefficient  while keeping the equation balanced.
    ::然后,将双方除以正确的数值,除去系数,同时保持方程式平衡。
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  • Click "Check" to see if you inputted the right values.
    ::单击“ 检查” 以查看您是否输入了正确的值 。
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  • Click "Reset" to change the what you added/subtracted back to zero.
    ::单击“ 重置” 将您添加/ 减缩的内容修改为零 。

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  As you noticed with the balance, you will need to undo the operations that are in the equation. You always undo the operations in the reverse order of the . Start with undo-ing addition and subtraction first, followed by multiplication and division. You need to isolate the variable . Here is a slightly more complicated example than those in the interactive.
  ::正如您在平衡中注意到的, 您需要撤销方程式中的操作。 您总是要以反向顺序撤消操作。 首先从撤消添加和减法开始, 然后是乘法和除法。 您需要分离变量。 这里的示例比互动中略为复杂 。

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  $$\begin{array}{rl}-\frac{1}{4}g+7=& -9\text{original equation, isolate }g\\ -7& -7\text{subtract 7 from both sides to undo the addition}\\ -4\times -\frac{1}{4}g=& -16\times -4\text{multiply both sides by -4 to undo the fraction}\\ g=& 64\end{array}$$

  
  ::- 14g+7+7+%%9 原始方程,从两侧分离 g-7 -7 -7 减去 7 以撤销添加 - 4\\ 14g\ _16 4 将两边乘以 - 4 以撤销分数g= 64

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  Notice that to undo the fraction , you would multiply by -4. This is the same as multiplying by the reciprocal of $\begin{array}{r}-\frac{1}{4}\end{array}$  because $\begin{array}{r}-\frac{4}{1}=-4\end{array}$ . Once you get the solution ,  make sure to check your work. Substitute in 64 for $\begin{array}{r}g\end{array}$  and see if the equation holds true:  $\begin{array}{r}-\frac{1}{4}(64)+7\to -16+7\to -9=-9.\end{array}$  This confirms that $\begin{array}{r}g=64\end{array}$  is the solution because the left side of the equation simplifies to be equal to the right side.
  ::注意要撤消分数, 您会乘以 - 4。 这与乘以- 14 的对等值相同, 因为- 41\\ 4。 一旦找到解决方案, 请确保检查您的作品 。 在 64 中将 g 替换, 并查看公式是否正确 : - 14( 64) + 7\ 16+7\\ 7\\ 9\ 9 。 这证实了 g= 64 是解决方案, 因为方程式的左侧简化为等于右侧 。

   

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  Work it Out 
  ::工作出来

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  There are three equations for you to solve in this interactive. The equation is at the top and you will p lace each step in order with the  correct  reasoning.
  ::在此互动中, 有三个方程式需要您解答 。 方程式位于顶端, 您将按正确的推理排列每个步骤 。

   

  

  INTERACTIVE

  Solving Two-Step Equations

  

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  • Rearrange the red and blue in the correct order to solve the equation at the top.
    ::将红色和蓝色重新排列为正确的顺序,以解析顶部方程式的方程。
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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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  • Click the buttons to switch between the different problems.
    ::单击按钮在不同问题之间切换。

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  Discussion Question
  ::讨论问题

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  Discuss with classmates how to solve $\begin{array}{r}4.3x-3.48=-\mathrm{1.33.}\end{array}$  Would you do anything differently because of the decimals? Why or why not?
  ::与同学讨论如何解析4.3x-3.481.33. 您会因为小数小数而做不同的事情吗? 为什么不行?

   

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     Summary
  ::摘要

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  • To solve an equation for a variable, you need to isolate it by undo-ing operations. Undo the operations in the reverse order of the Order of Operations. 
    ::要解析变量的方程式, 您需要通过撤消操作来分离变量。 按操作命令的反序撤消操作 。
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  • Sometimes the first step will be to apply the Distributive Property or combine like terms on the side with the variable. 
    ::有时第一步将是适用分配财产,或将类似条件与变量结合起来。
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  • Do not undo operations until there is one variable term and one constant on the side of the equation with the variable. 
    ::在变量的方程式侧面有一个变量术语和一个常数之前,不撤销操作 。
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  • When the coefficient is a fraction, multiply both sides by its reciprocal to undo it.
    ::当系数是分数时,将双方乘以对等系数来取消系数。