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Solution procedures | Lesson

What are solution procedures?

In general, a procedure is a sequence of mathematical operations carried out in order.
A solution procedure is a sequence of steps that, when taken, solves an equation.
Procedures can also be visualized as flowcharts, where each step is connected by arrows.
Both verbal procedures and flowcharts can be reversed, which lets us trace our steps from the end of a procedure to the beginning.
Finally, we can repeat the same procedure to generate numbers in a sequence.

What skills are tested?

  • Identifying the solution procedure for a linear equation with one variable
  • Identifying operations that reverse a sequence of steps
  • Following a flowchart to calculate a result
  • Reversing a flowchart to calculate the input given the result
  • Finding terms in a recursive sequence

How do we write solution procedures?

To write the steps to solve an equation, identify the
inverse operations
we need to perform on both sides of the equation until the variable is left by itself and write verbal descriptions describing each.
  • Addition and subtraction are inverse operations.
  • Multiplication and division are inverse operations.

How do we reverse a procedure?

To reverse a procedure made up of a sequence of operations, we must write an inverse operation for each forward operation. Then, we need to perform the inverse operations in reverse order.

What's a flowchart?

A flowchart is a visual representation of a sequence of operations. Each operation is applied to the result of the previous operation.
To find the result of a flowchart given the input, carry out all of the operations in the flowchart in order.
To find the input of a flowchart given the result, find the inverse operation for each operation in the flowchart, then carry out all of the inverse operations in reverse order starting with the result.

What's a recursive sequence?

In a recursive
sequence
, the
terms
beyond the first one(s) are generated based on the values of the preceding terms. This means carrying out operations on the previous term to calculate the next term.
For each subsequent term, the operations remain the same, but the input changes, e.g., the 2nd term is calculated using the 1st term, the 3rd term is calculated using the 2nd term, etc.

Your turn!

TRY: STATING THE SOLUTION PROCEDURE
Which of the following sequence of steps, when completed, will solve the equation 6, x, minus, 7, equals, 8 for x ?
Choose 1 answer:
Choose 1 answer:

TRY: IDENTIFYING THE FIRST SOLUTION STEP
Which of the following would be a logical and correct first step in solving the equation 4, x, plus, 8, equals, 20 ?
Choose 1 answer:
Choose 1 answer:

TRY: REVERSING STEPS IN A FLOWCHART
If the result printed according to the flowchart above is 11, what was the value of the input x ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

TRY: CALCULATING TERMS IN A RECURSIVE SEQUENCE
The first term in a recursive sequence is 1. Each subsequent term in the sequence is calculated by multiplying the previous term by 3 and subtracting 1 from the result. Which of the following are terms in the sequence?
Choose all answers that apply:
Choose all answers that apply:

Things to remember

A solution procedure is a verbal description of the steps we take to solve an equation.
To reverse a procedure, perform the inverse operations in reverse order.
A flowchart is a visual representation of a sequence of operations.
  • To calculate the result given the input, perform the operations in order.
  • To calculate the input given the result, perform the inverse operations in reverse order.
A recursive sequence generates each subsequent term by carrying out the stated operations on the preceding term.

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