I dont understand why on number one, you added 7 on both sides but only really added it to 8. why were the 7's on the other side completely forgotten?

You add +7 to the -& to get rid of that. And anything you do on one side you have to do on the other side for it to balance. So -7 +7 = 0 and then 8 + 7 = 15

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Solution procedures | Lesson

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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.

Let's say the first term of a sequence is

2

, and each subsequent term is generated by adding

2

to the previous term.

The first few terms of the sequence are:

Term	Number
$1$ ‍st	$2$ ‍
$2$ ‍nd	$2 + 2 = 4$ ‍
$3$ ‍rd	$4 + 2 = 6$ ‍
$4$ ‍th	$6 + 2 = 8$ ‍
$5$ ‍th	$8 + 2 = 10$ ‍

Adding 2 to the previous term

" is the procedure we follow to generate the sequence above.

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

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.

A positive integer is multiplied by

3

, and then

1

is added to the result.

The forward operations are:

Step	Operator	Number
$1 st$ ‍	$multiply$ ‍	$3$ ‍
$2 nd$ ‍	$add$ ‍	$1$ ‍

To reverse the procedure, we need to perform the inverse operations in reverse order:

Step	Operator	Number
$1 st$ ‍	$subtract$ ‍	$1$ ‍
$2 nd$ ‍	$divide$ ‍	$3$ ‍

In words, the reverse procedure that gets us from the final number to the positive integer in the beginning is:

Subtract $1$ ‍ from the final number
Divide the result by $3$ ‍

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

, the

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

2

nd term is calculated using the

1

st term, the

3

rd term is calculated using the

2

nd term, etc.

The first term of a recursive sequence is

3

. Each subsequent term is calculated by multiplying the previous term by

2

The table below shows how to generate the first few terms of the sequence.

Term	Value
$1$ ‍st	$3$ ‍
$2$ ‍nd	$3 \times 2 = 6$ ‍
$3$ ‍rd	$6 \times 2 = 12$ ‍
$4$ ‍th	$12 \times 2 = 24$ ‍
$5$ ‍th	$24 \times 2 = 48$ ‍

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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grandmagnolia1
Posted 3 years ago. Direct link to grandmagnolia1's post “I dont understand why on ...”
I dont understand why on number one, you added 7 on both sides but only really added it to 8. why were the 7's on the other side completely forgotten?
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- Brenda-Jean Rice
  Posted 3 years ago. Direct link to Brenda-Jean Rice's post “You add +7 to the -& to g...”
  You add +7 to the -& to get rid of that. And anything you do on one side you have to do on the other side for it to balance. So -7 +7 = 0 and then 8 + 7 = 15
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Shekhar Maheshwari
Posted 3 years ago. Direct link to Shekhar Maheshwari's post “What grade is this for”
What grade is this for
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LUCY BELL
Posted 6 months ago. Direct link to LUCY BELL's post “how is this easy?”
how is this easy?
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Course: Praxis Core Math > Unit 1