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

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 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.

THE ORDER OF OPERATIONS (Topmost First)
• Functions
• Parentheses or other Marks of Inclusion (Innermost First)
• Roots or Exponents
• Multiplication or Division (Leftmost First)
• Addition or Subtraction (Leftmost 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.

 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 3.)     2x - 5 = 4 4.)     15 = 3y + 12 5.)     -4(x + 2) + 3 = -2 6.)     x/3 - 5 = 10 7.)     x = 6 + 3 - 2x + 2x For example, solve:   3 + 2x = 4x - 1 © 2007, A2, www.mathnstuff.com/math/algebra/asolin2.htm     