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## Praxis Core Math

### Unit 1: Lesson 4

Algebra- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example
- Algebraic word problems | Lesson
- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

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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

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

, 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 2nd term is calculated using the 1st term, the 3rd term is calculated using the 2nd term, etc.

## Your turn!

## 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.

## Want to join the conversation?

- 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?(1 vote)
- 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(3 votes)

- What grade is this for(2 votes)