Substitution

Algebra: Variables

Substitution

If a variable occurs in an expression, you can enter any number for that variable. In other words, replace every occurrence of that variable in the expression by a number.

This process is called substitution.

Example

Calculate #\blue{x}^2+\blue{x}# for #\blue{x}=\green{3}#:

\[{\blue{x}^2+\blue{x}=}{\green{3}^2+\green{3}}{=12}\]

Substituting a negative number

Note: If you are substituting a negative number, placing brackets around the number can be convenient.

If you do not place #\green{-2}# in the example at the right-hand side in between brackets, you will have a different answer since #-2^2=-4#.

Example

Calculate #\blue{x}^2# for #\blue{x}=\green{-2}#:

\[{\blue{x}^2=} {(\green{-2})^2}{=4}\]

You can enter any number for a variable, as long as it makes sense mathematically.

In the expression #\sqrt{\green y-3}# it's not possible to enter the number #\green 2# because it's not possible to take the root of a negative number.

In the expression#\tfrac{1}{\purple{z}}# it's not possible to enter the number #\purple{0}# for #\purple z#, since dividing by #\purple 0# is not possible.

Calculate #{{x}\over{-x^2-x+5}}# for #x=3#. Simplify the answer to a number or fraction.

#-{{3}\over{7}}#

#\begin{array}{rcl}
\displaystyle {{x}\over{-x^2-x+5}} &=& \displaystyle{{3}\over{-3^2-3+5}} \\
&&\blue{\text{\(x\) replaced with \(3\)}}\\
&=& \displaystyle -{{3}\over{7}} \\
&&\blue{\text{calculated}}\\
\end{array}#

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