Course: 7.11 口音模型的双级两等

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口音模型的双级两等
Kara works as a babysitter for the neighborhood she lives in. She is saving money to plant an amazing sustainable home garden. For each babysitting job she took on, Kara charged $4 for bus fare plus an additional $8 for each hour she worked. On Saturday, Kara earned $26 for the entire babysitting job.
::Kara是她居住的邻居的保姆。她正在储蓄钱来种植一个令人惊叹的可持续家庭花园。她每次做保姆都收取4美元的公交费,每工作一小时加8美元。星期六,Kara为整个保姆工作挣了26美元。

Write an equation to represent this situation, where $\begin{aligned} h \end{aligned}$ is the total number of hours that Kara worked.
::写一个方程式来代表这种情况, 这里的h是卡拉工作的小时总数。

In this concept, you will learn to write two-step equations from verbal models.
::在这个概念中,你将学会从口头模型中写出两步方程。

Writing Two-Step Equations from Verbal Models
::从口音模式书写双级等式

You solve equations like $\begin{aligned} 3 x = 5, \frac{x}{- 2} = - 4 \end{aligned}$ , and $\begin{aligned} x + 31 = 8 \end{aligned}$ by doing one operation to both sides of the equation to isolate the variable .
::您对方程式的两侧做一个操作以分离变量, 从而解析方程式, 如 3x=5, x- 24 和 x+31=8 等方程式。

But how can you solve the following equations?
::但是,你怎么解决以下方程式的问题呢?

$\begin{aligned} \begin{array}{rcl} 3 x + 5 & = & 20 \\ \frac{x}{3} - 2 & = & 5 \end{array} \end{aligned}$

::3x+5=20x3-2=5

In these equations you need to do two operations to each side of the equation to isolate the variable. However, before you do this, look at some examples of word problems that involve two steps.
::在这些方程式中,您需要对方程式的每侧进行两次操作,以孤立变量。然而,在这样做之前,请先看看涉及两步的字词问题实例。

Here is an example.
::举一个例子。

Change the following word problem into an equation.
::将以下字词问题修改为等式。

Six times a number, plus five is forty-one.
::6倍一个数字,加5是41。

First, change the language into number and symbols. “Times” means multiplication , “a number” since it is not identified is your variable $\begin{aligned} x \end{aligned}$ , “plus” means addition , and the word “is” means equals.
::首先,将语言改为数字和符号。“时间”是指乘法,“数字”是指“数字”,因为它没有被识别为变量x,“附加”是指添加,“是”是指等值。

$\begin{aligned} 6 x + 5 = 41 \end{aligned}$

::6x+5=41

The answer is $\begin{aligned} 6 x + 5 = 41 \end{aligned}$ .
::答案是6x+5=41。

Here is another example.
::下面是另一个例子。

Change the following word problem into an equation.
::将以下字词问题修改为等式。

Four less than two times a number is equal to eight.
::4比2乘以一个数字等于8。

First, change the language into an equation. “Less than” means subtraction but be careful about the order . “Times” means multiplication, “a number” is your variable $\begin{aligned} x \end{aligned}$ , and “is equal to” means the same thing as equals.
::首先,将语言修改为等式。“慢于”是指减法,但注意顺序。“时间”是指乘法,“数字”是指变量x,“数字”是指等同。

$\begin{aligned} 2 x - 4 = 8 \end{aligned}$

::2x-4=8

The answer is $\begin{aligned} 2 x - 4 = 8 \end{aligned}$ .
::答案是 2x-4=8。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Kara’s sustainable garden.
::更早之前, Kara的可持续花园给您带来了问题。

She is saving money to build one at home. She has a babysitting job where she earns $8 and hour, but she also charges $4 for bus fare. If she earned $26 in total, can you write and equation to represent this.
::她在家里存钱建造一个。她有一份保姆工作,挣8美元和小时,但她也收取4美元的公共汽车费。如果她总共挣26美元,你可以写和等式来代表这一点。

First, let $\begin{aligned} h \end{aligned}$ be the number of hours Kara worked.
::首先,让我们看看卡拉工作的小时数。

Next, re-phrase the text to make it easier to understand. Her total earnings were $4 plus the number of hours she worked times 8. This equals $26 the total amount earned.
::其次,重新起草案文,以便更容易理解。她的总收入为4美元,加上她工作时数的8倍。这等于收入总额26美元。

Then, turn the language into numbers and symbols and write the equation. “Plus” means addition, “the number of hours” is the variable $\begin{aligned} h \end{aligned}$ , “times” means multiplication.
::然后,将语言变成数字和符号,并写出方程式。“加”意指添加,“小时数”是变量h,“时间”意指乘法。

$\begin{aligned} 4 + 8 h = 26 \end{aligned}$

::4+8小时=26

The answer is $\begin{aligned} 4 + 8 h = 26 \end{aligned}$ .
::答案是4+8h=26。

Example 2
::例2

Write an equation for this statement.
::为此语句写一个方程。

A number divided by two, and then added to six is equal to fourteen.
::数字除以2,然后加为6,等于14。

First, change the language into numbers and mathematical symbols. “A number” is your variable $\begin{aligned} x \end{aligned}$ , “divided by” means division , “and then added to” means that after you divide you add, and “is” means equals.
::首先,将语言修改为数字和数学符号。“一个数字”是变量x,“由”是指除法,“然后添加到”是指在分隔后添加,“是”是指等值。

Then, write the equation.
::那就写个方程式吧

$\begin{aligned} \frac{x}{2} + 6 = 14 \end{aligned}$

::x2+6=14

The answer is $\begin{aligned} \frac{x}{2} + 6 = 14 \end{aligned}$ .
::答案是 x2+6=14 。

Write an equation for each word problem.
::为每个字的问题写一个方程。

Example 3
::例3

The product of five and a number, plus three is twenty-three.
::5和数字的产物,加3是23。

First, translate the language into numbers and symbols. “The product of” means multiply what is in the parenthetical expression “five and a number,” “a number” is your variable $\begin{aligned} x \end{aligned}$ , “plus” means addition, and “is” means equals.
::首先,将语言翻译为数字和符号。“的产物”是指括号中的“5和数字”中的乘数,“数字”是指变量x,“附加”是指添加,“是”是指等值。

Then, write your equation.
::那就写你的方程式吧

$\begin{aligned} 5 x + 3 = 23 \end{aligned}$

::5x+3=23

The answer is $\begin{aligned} 5 x + 3 = 23 \end{aligned}$ .
::答案是5x3+3=23。

Example 4
::例4

Six times a number, minus four is thirty-two.
::数字六倍,减四是三十二

First, translate the language into numbers and symbols. “Times” means multiplication, “a number” is the variable $\begin{aligned} x \end{aligned}$ , “minus” means subtraction, and “is” means equals.
::首先,将语言翻译为数字和符号。“时间”是指乘法,“数字”是指变量x,“减去”是指减法,“是”是指等值。

$\begin{aligned} 6 x - 4 = 32 \end{aligned}$

::6x-4=32

The answer is $\begin{aligned} 6 x - 4 = 32 \end{aligned}$ .
::答案是6x-4=32。

Example 5
::例5

A number $\begin{aligned} y \end{aligned}$ , divided by 3, and then added to seven is ten.
::A Y,除以3,然后加到7是10。

First, translate the language into numbers and symbols. “A number $\begin{aligned} y \end{aligned}$ ” is your variable $\begin{aligned} y \end{aligned}$ , “and then added to” means you divide and then add, and “is” means equals.
::首先,将语言翻译为数字和符号。“A number y”是变量y,“然后添加到”是指分隔和添加,“是”是指等值。

$\begin{aligned} \frac{y}{3} + 7 = 10 \end{aligned}$

::y3+7=10 y3+7=10

The answer is $\begin{aligned} \frac{y}{3} + 7 = 10 \end{aligned}$ .
::答案是 y3+7=10。

Review
::回顾

Write each statement as two-step equations.
::将每个语句作为两步方程书写。

Two times a number, plus seven is nineteen.
::两个数字乘以两个数字,加7是19。

Three times a number, and five is twenty.
::三次一个数字, 5是20。

Six times a number, and ten is forty-six.
::6次一个数字,10是46。

Seven less than two times a number is twenty-one.
::7比2乘以2 数字是21

Eight less than three times a number is sixteen.
::8比3乘以1是16。

A number divided by two, plus seven is ten.
::数字除以二,加七是十

A number divided by three, and six is eleven.
::数除以三,六是十一

Two less than a number divided by four is ten.
::两个小于一个数字除以四个是十个。

Four times a number, and eight is twenty.
::4倍一个数字,8是20。

Five times a number, take away three is twelve.
::5次一个数字, 取走3是12。

Two times a number, and seven is twenty-nine.
::数字两次,7是29。

Four times a number, and two is twenty-six.
::4倍一个数字,2是26。

Negative three times a number, take a way four is equal to negative ten.
::负乘以3乘以1乘以4等于负乘以10

Negative two times a number, and eight is equal to negative twelve.
::负乘以二,八等于负十二

Negative five times a number, minus eight is equal to seventeen.
::负5乘以1个数字,负8等于17。

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

General

口音模型的双级两等

Writing Two-Step Equations from Verbal Models ::从口音模式书写双级等式

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Writing Two-Step Equations from Verbal Models
::从口音模式书写双级等式

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源