Section: 单变量表达式 | 1.4单变量表达式

Section outline

Shelly is making bracelets to sell at her town's market this summer. She spent $150 on supplies and will make $4 for every bracelet she sells. Her profit for selling $\begin{aligned} b \end{aligned}$ bracelets is given by the expression $\begin{aligned} 4 b - 150. \end{aligned}$ How can Shelly calculate her profit if she sells 50 bracelets this summer?
::Shelly今年夏天在市集市场做手镯,她花150美元购买用品,每卖一个手镯就挣4美元,出售b手镯的利润由4 b - 150表示给予。 Shelly今年夏天卖50个手镯又如何计算利润?

In this concept, you will learn how to evaluate single variable expressions.
::在此概念中,您将学习如何评价单个变量表达式。

Evaluating Single Variable Expressions
::评价单变量表达式

An expression is a mathematical phrase that contains numbers and operations .
::表达式是一个包含数字和操作的数学短语。

Here are some examples of expressions:
::以下是一些表达方式的例子:

$\begin{aligned} 3 + 10 - 5 \end{aligned}$

$\begin{aligned} - 15 + 7 - 1 \end{aligned}$

$\begin{aligned} 5^{2} - 1 \end{aligned}$

$\begin{aligned} 15 (3 + 4) + 2 \end{aligned}$

A variable is a symbol or letter (such as $\begin{aligned} x, m, R, y, P \end{aligned}$ , or $\begin{aligned} a \end{aligned}$ ) that is used to represent a quantity that might change in value. A variable expression is an expression that includes variables. Another name for a variable expression is an algebraic expression .
::变量是一个符号或字母(例如 x、 m、 R、 y、 P 或 ),用来表示值可能变化的数量。变量表达式是一个包含变量的表达式。变量表达式的另一个名称是代数表达式。

Here are some examples of variable expressions:
::以下是一些变量表达式的例子:

$\begin{aligned} 3 x + 10 \end{aligned}$
::3 x + 10 3 x + 10

$\begin{aligned} 10 r \end{aligned}$
::10 r 10 r

$\begin{aligned} b^{3} + 2 \end{aligned}$
::b 3+2 b 3+2

$\begin{aligned} m x - 3 \end{aligned}$
::m x x - 3

A single variable expression is a variable expression with just one variable in it.
::单个变量表达式是一个变量表达式,其中只有一个变量。

You can use a variable expression to describe a real world situation where one or more quantities has an unknown value or can change in value.
::您可以使用变量表达式来描述一个或一个以上数量值未知或值可能变化的真实世界状况。

To evaluate a variable expression means to find the value of the expression for a given value of the variable. To evaluate, substitute the given value for the variable in the expression and simplify using the . To follow the order of operations, you always need to do any multiplication/ division first before any addition/ subtraction .
::要对变量表达式进行评价, 需要为变量的某个值查找表达式的值。要对变量进行评审, 请将给定值替换为表达式中的变量, 并简化使用。要遵循操作的顺序, 您总是需要在增加/ 减法之前先做任何倍增/ division 。

Here is an example.
::举一个例子。

Evaluate the expression $\begin{aligned} 10 k - 44 \end{aligned}$ for $\begin{aligned} k = 12 \end{aligned}$ .
::评估表达式 10 k - 44 k = 12 。

First, remember that when you see a number next to a letter, like " $\begin{aligned} 10 k \end{aligned}$ ", it means to multiply.
::首先,记住,当你看到信旁边的号码,如 " 10k " ,这意味着乘法。

Next, substitute 12 in for the letter $\begin{aligned} k \end{aligned}$ in the expression.
::接下来,在表达式中的字母 k 中替换12 。

Notice that you can put " data-term="Parentheses" role="term" tabindex="0"> parentheses around the 12 to keep it separate from the number 10.
::请注意,您可以把12号前后的括号加在括号上,以便将其与10号分开。

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
::现在, 使用操作顺序简化表达式。您需要先乘再减去。

The answer is 76.
::答案是76个

Here is another example that involves division.
::下面是涉及分裂的另一个例子。

Evaluate the expression $\begin{aligned} \frac{x}{3} + 2 \end{aligned}$ for $\begin{aligned} x = 24 \end{aligned}$ .
::评估表达式 x 3 + 2 x = 24 。

First, remember that a fraction bar is like a division sign. $\begin{aligned} \frac{x}{3} \end{aligned}$ is the same as $\begin{aligned} x \div 3 \end{aligned}$ .
::首先, 记住一个分数栏就像一个分隔符。 x 3 和 x { 3 相同。

Next, substitute 24 in for the letter $\begin{aligned} x \end{aligned}$ in the expression.
::接下来,在表达式中的字母 x 中替换24。

Now, simplify the expression using the order of operations. You will need to divide first and then add.
::现在, 使用操作顺序简化表达式。您需要先分隔, 然后添加。

The answer is 10.
::答案是10个

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Shelly and her bracelet business.
::早些时候,你得到一个问题关于雪莉和她的手镯业务。

Shelly is selling bracelets this summer and her profit for selling $\begin{aligned} b \end{aligned}$ bracelets is given by the expression $\begin{aligned} 4 b - 150. \end{aligned}$ Shelly wants to calculate what her profit will be if she sells 50 bracelets.
::Shelly今年夏天出售手镯,她出售b手镯的利润由4 b - 150的表达方式提供。 Shelly想计算她出售50个手镯的利润。

To calculate her profit from selling 50 bracelets, Shelly needs to evaluate the expression $\begin{aligned} 4 b - 150 \end{aligned}$ for $\begin{aligned} b = 50. \end{aligned}$
::为了计算她出售50个手镯的利润, Shelly需要评估4 b - 150 = 50 = 50 = b = 50 = = 4 b - 150。

First, substitute 50 in for the letter $\begin{aligned} b \end{aligned}$ in the expression.
::首先,用50取代表达式中的b字母。

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
::现在, 使用操作顺序简化表达式。您需要先乘再减去。

Shelly's profit from selling 50 bracelets would be $50.
::卖50个手镯雪莉的利润是50美元

Example 2
::例2

Evaluate $\begin{aligned} \frac{x}{7} - 5 \end{aligned}$ if $\begin{aligned} x \end{aligned}$ is 49.
::评价x7 - 5,如果x49。

First, substitute 49 in for the letter $\begin{aligned} x \end{aligned}$ in the expression.
::首先,用49取代表达式中的字母x。

Now, simplify the expression using the order of operations. You will need to divide first and then subtract.
::现在, 使用操作顺序简化表达式。您需要先分隔, 然后减去。

The answer is 2.
::答案是2。

Example 3
::例3

Evaluate $\begin{aligned} 4 x - 9 \end{aligned}$ if $\begin{aligned} x \end{aligned}$ is 20.
::如果x为20,评价4x-9。

First, substitute 20 in for the letter $\begin{aligned} x \end{aligned}$ in the expression.
::首先,在表达式中的字母 x 中替换20。

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.
::现在, 使用操作顺序简化表达式。您需要先乘再减去。

The answer is 71.
::答案是71岁

Example 4
::例4

Evaluate $\begin{aligned} 5 y + 6 \end{aligned}$ if $\begin{aligned} y \end{aligned}$ is 9.
::如果y为9,评价5y+6。

First, substitute 9 in for the letter $\begin{aligned} y \end{aligned}$ in the expression.
::首先,用字母 Y 的 9 替换表达式中的 y 。

Now, simplify the expression using the order of operations. You will need to multiply first and then add.
::现在, 使用操作顺序简化表达式。您需要先乘再添加。

The answer is 51.
::答案是51岁

Example 5
::例5

Evaluate $\begin{aligned} \frac{a}{4} - 8 \end{aligned}$ if $\begin{aligned} a \end{aligned}$ is 36.
::评估4 - 8,如果是36。

First, substitute 36 in for the letter $\begin{aligned} a \end{aligned}$ in the expression.
::首先,以36取代A字中的36。

Now, simplify the expression using the order of operations. You will need to divide first and then subtract.
::现在, 使用操作顺序简化表达式。您需要先分隔, 然后减去。

The answer is 1.
::答案是 1 。

Review
::回顾

Evaluate each expression if the given value of $\begin{aligned} r \end{aligned}$ is 9.
::如果 r 的给定值为 9 , 对每种表达式进行评价。

$\begin{aligned} \frac{r}{3} \end{aligned}$
::3 r 3

$\begin{aligned} 63 - r \end{aligned}$
::63 - r

$\begin{aligned} 11 r \end{aligned}$
::11 r 11 r

$\begin{aligned} 2 r + 7 \end{aligned}$
::2 r + 7 2 r + 7

$\begin{aligned} 3 r + r \end{aligned}$
::3 r + r

$\begin{aligned} 4 r - 2 r \end{aligned}$
::4 r- 2 r

$\begin{aligned} r + 5 r \end{aligned}$
::r + 5 r

$\begin{aligned} 12 r - 1 \end{aligned}$
::12 r- 1

Evaluate each expression for $\begin{aligned} h = 12 \end{aligned}$ .
::h=12,评价每个表达式。

$\begin{aligned} 70 - 3 h \end{aligned}$
::70 - 3小时

$\begin{aligned} 6 h + 6 \end{aligned}$
::6小时+6小时

$\begin{aligned} 4 h - 9 \end{aligned}$
::4 h- 9( 4 h- 9)

$\begin{aligned} 11 + \frac{h}{4} \end{aligned}$
::11 + h 4 11 + h 4

$\begin{aligned} 3 h + h \end{aligned}$
::3小时+小时

$\begin{aligned} 2 h + 5 h \end{aligned}$
::2小时+5小时

$\begin{aligned} 6 h - 2 h \end{aligned}$
::6小时-2小时

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

Evaluating Single Variable Expressions ::评价单变量表达式

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

Evaluating Single Variable Expressions
::评价单变量表达式

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