solve linear equation w/more than one operation in the expression, pg 2

Contents & Resource Pages:  
Solve:   x - 6 = -12       Solve:   x + 6 = -12       Solve:   x/6 = -12       Solve:   6x = -12

Solve:   - x = -12       Solve:   5x/6 = -12       Solve:   3 + 2x = - 1

Solve:   3 + 2x = 4x - 1      Solve:   3x + 4(x -1) = 2      Solve:   4x + 2 - 3x + 5 - 2(x + 5) = (2x - 5) + (3x + 4)
consecutive integer expressions, equations       Solving Equation on Graphing Calculators

Intro to Solving Linear Equations                   One Operation Equations  
More Than One Operation Equations           Solve Linear Equation w/Many Operations 
Solutions to a Linear Equation & Solving Linear Equations Graphically
Linear Equation Solver - The Page Does The Work


 
More Than One Operation Equations
 
Solve:   3 + 2x = - 1

      To solve a linear equation with more than one operation, one must undo the operations in reverse of the order of order of operations.

      As listed below, the topmost operation has priority when simplifying an expression. In solving an equation, the bottommost function generally must be undone first.

      In the expression 3 + 2x, the x is first multiplied by 2, then 3 is added to the result.

      Restated, 3 + 2x means, 1st: multiplied x by 2, 2nd: add 3 to the result.

      To solve the equation 3 + 2x = -1, 1st: undo the addition, 2nd: undo the multiplication.

1.) Solve:  
3 + 2x = - 1
- 3         = - 3
------------------------
      2x = - 4
      2x/2 = - 4/2
      x = - 2

How do you undo adding 3? SUBTRACT 3.


How do you undo multiplying by 2? DIVIDE BY 2.

2.) Solve:  
3x + 4(x -1) = 2
3x + 4x - 4 = 2
7x - 4 = 2
     + 4 = + 4
------------------------
      7x = + 6
      7x/7 = + 6/7
      x = 6/7

How do you undo multliplying 4 by (x - 1)? DISTRIBUTE THE 4*.
How do you combine the 3x and the 4x? JUST COMBINE LIKE TERMS.
How do you undo subtracting 4? ADD 4.


How do you undo multiplying by 7? DIVIDE BY 7.
      * The phrase 4(x-1) and the quest to "undo multliplying 4 by (x - 1)?" may be confusing. The expression 4(x-1) is written in factored form. The expression 4x - 4 is an equivalent expression written in unfactored form. To write 4(x-1) as 4x - 4, one distributes.

Solve. MouseOver for answers.
      Describe how to solve the equation, then state the solution.
      Use terms such as divide by a number, add a number, combine like terms, distribute, to get x = some constant.
 
ex. 2 above.) Solve 3x + 4(x -1) = 2 distribute, add 4, divide by 7, to get x = 6/7
 
3.)     2x - 5 = 4     add 5, divide by 2, to get x = 9/2
 
4.)     15 = 3y + 12     subtract 12, divide by 3, to get y = 1
 
5.)     -4(x + 2) + 3 = -2     distribute the -4, combine like terms, add 5, divide by -4, to get x =3/4
 
6.)     x/3 - 5 = 10     add 5, multiply by 3, to get x = 45
 
7.)     x = 6 + 3 - 2x + 2x     combine like terms , to get x = 9
 


Solve linear equation w/many operations

For example, solve:   3 + 2x = 4x - 1      

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