章节大纲

  • Multiple Variable Expressions 
    ::多个变量表达式

    A common activity in Algebra is to simplify an expression by   evaluating  it for some given value of the variable .
    ::代数中的常见活动是通过对变量的某个给定值进行评价来简化表达式。

    Take a look at this example to see how this works:
    ::看看这个例子,看看它是如何运作的:

    Let x = 12. Find the value of 2x - 7.
    ::Let x = 12. 查找 2x - 7 的值 。

    To find the solution, substitute 12 in place of  x in the given expression.
    ::为了找到解决办法,代之以12,代替给定表达式中的x。

    2 x − 7 = 2 ( 12 ) − 7 = 24 − 7 = 17

    ::2x-7=2(12)-7=24-7=17

    Note: In the first step of the problem, keep the substituted value in " data-term="Parentheses" role="term" tabindex="0"> parentheses . This makes the written-out problem easier to follow, and helps avoid mistakes. For instance, i f you didn’t use parentheses, you could end up turning  2 x − 7  into  212 − 7 ,  instead of  2 × 12 − 7 !
    ::注意: 在问题的第一步中, 请将替代值保留在括号中 。 这样可以让写出的问题更容易跟踪, 并有助于避免错误 。 例如, 如果您不使用括号, 最终可能会把 2x-7 变成 212-7 , 而不是 2x12-7 !

    Evaluating an Expression 
    ::评价表达式

    Let y = − 2. Find the value of 7 y − 11 y + 2.

    ::让 y% 2 查找 7y- 11y+2 的值 。

    7 ( − 2 ) − 11 ( − 2 ) + 2 = − 3 1 2 + 22 + 2 = 24 − 3 1 2 = 20 1 2

    Many expressions have more than one variable in them. For example, the formula for the perimeter of a rectangle, P = 2 l + 2 w , has two variables: length ( l ) and width ( w ) .  Be careful to substitute the appropriate value in the appropriate place.
    ::许多表达式都有多个变量。 例如, 矩形周围的公式 P=2l+2w, 有两个变量: 长度( l) 和宽度( w) 。 注意在合适的地方替换合适的值 。

    Evaluating an Expression with Multiple Variables
    ::以多个变量评价表达式

    The area of a trapezoid is given by the equation A = h 2 ( a + b ) . Find the area of a trapezoid with bases a = 10   c m and b = 15   c m and height h = 8   c m .
    ::方程式 A=h2(a+b) 给定捕捉类动物的区域。 查找以碱a=10厘米和b=15厘米和高度 h=8厘米为基点的捕捉类动物的区域。

    To find the solution to this problem, substitute the given values for variables a ,   b , and h  in place of the appropriate letters in the equation.
    ::为了找到解决这个问题的办法,用给定值代替变量a、b和h,以代替方程式中适当的字母。

    A = h 2 ( a + b )  Substitute  10  for  a ,   15  for  b ,   and  8  for  h . = ( 8 ) 2 ( ( 10 ) + ( 15 ) ) Evaluate piece by piece.  10 + 15 = 25  and  8 2 = 4. = 4 ( 25 ) A = 100
    ::A=h2(a+b) a的替代物10, b的替代物15, b的替代物10, h=(8)2((10)+(15))的替代物8, h=(8)2((10)+(15)的替代物10, 10+15=25, 82=4.=4(25)A=100

    Example
    ::示例示例示例示例

    Example 1
    ::例1

    Let x = 3 and y = − 2. Find the value of 3 x y + 6 y − 2 x .
    ::Let x=3 and y2. 查找 3xy+6y-2x 的值。

    3 x y + 6 y − 2 x = 3 ( 3 ) ( − 2 ) + 6 ( − 2 ) − 2 ( 3 ) = ( − 18 ) + ( − 3 ) − ( 6 ) = − 27

    ::3xy+6y-2x=3(3)(3)--2)+6(-2)-2(3)=(-18)+(-3)-(6)-(6)-__27

    Review 
    ::回顾

    Evaluate questions 1 through 8, using a = − 3 ,   b = 2 ,   c = 5 , and d = − 4.
    ::使用a+3,b=2,c=5和d++++4评价问题1至8。

    1. 2 a + 3 b
      ::2a+3b
    2. 4 c + d
      ::4c+d 4c+d
    3. 5 a c − 2 b
      ::5ac-2b
    4. 2 a c − d
      ::2-d
    5. 3 b d
      ::3bd 3bd
    6. a − 4 b 3 c + 2 d
      ::a-4b3c+2d
    7. 1 a + b
      ::1a+b
    8. a b c d
      ::abcd abcd

    For questions 9 through 11, the weekly cost C of manufacturing x remote controls is given by the formula C = 2000 + 3 x , where the cost is given in dollars.
    ::关于问题9至问题11,制造x遥控的每周费用C由公式C=2000+3x提供,其费用以美元计算。

    1. What is the cost of producing 1000 remote controls?
      ::生产1000个遥控器的成本是多少?
    2. What is the cost of producing 2000 remote controls?
      ::生产2000年遥控装置的成本是多少?
    3. What is the cost of producing 2500 remote controls?
      ::生产2500个遥控器的成本是多少?

    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 。