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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

In this page, algebraic equation is introduced as a statement of two algebraic expressions, or a statement of equating an algebraic expression to a number.



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Numerical equation is a statement equating two numerical expressions.

    →  eg: `2+4-1 = 5`
Note that `2+4-1` is evaluated to `6-1` which equals `5`.

    →  eg: `4xx3-7 = 2+4-1`
Note that both sides can be evaluated to `5`

Numerical equations are not studied in detail, as the arithmetic can be performed to a number as result.

Learning the similarity of Numerical equations and Algebraic equations helps to understand algebraic equations better.

In this pattern of squares using crayons, if the number of squares in a row is `x`, the number of crayons forming the squares `=3x+1`. square using crayons one row Someone used `22` crayons to create such a pattern. How many squares will be made?

  • given number of crayons, the number of squares cannot be calculated
  • equate the number of crayons to the algebraic expression
  • equate the number of crayons to the algebraic expression

The answer is 'equate the number of crayons to the algebraic expression'. This is explained in the next page.

The number of crayons forming `x` squares `=3x+1`. Someone used `22` crayons to create a similar pattern. square using crayons one row The question provides that the "number of crayons used `= 22`"

We know that "the number of crayons forming squares `= 3x+1`"

Both the above are number of crayons and so can be equated.

`3x+1=22`.

This is an example of algebraic equation.

Which of the following is a meaning for the word 'equation'?

  • an imaginary line along the center of the Earth
  • a statement that two quantities are equal
  • a statement that two quantities are equal

The answer is 'a statement that two quantities are equal'.

What is the word or phrase used to refer a statement that two quantities are equal?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'algebraic equation'.

Algebraic equation is a statement that two quantities, represented with one or more variables, are equal.

An algebraic equation has the following.

 •  an equal symbol `=`

 •  a quantity on the left hand side (LHS) of the equal symbol.

 •  another quantity on the right hand side (RHS) of the equal symbol.

 •  One of the quantities on LHS or RHS is an algebraic expression.

 •  The other is in the form of algebraic expression or numerical expression or a number.

What is the terms used to refer either side of equation?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'left hand side (LHS) and right hand side (RHS)'.

Algebraic Equation : A statement equating two expressions is an algebraic equation.

`text(expression1) = text(expression2)`

expression1 is the left hand side (LHS) of the equation.

expression2 is the right hand side (RHS) of the equation.

                            
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