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Substitution into Algebraic Expressions I


In algebra, we use letters to represent unknown values, and we call these unknowns variables or pronumerals. For example if we know that $x+2=5$x+2=5, then we can work out that $x=3$x=3 since we also know that $3+2=5$3+2=5.

Sometimes we want to do this process in reverse, however, and we substitute numbers into equations in place of variables to determine a final value. We can substitute in any kinds of numbers, including whole numbers, decimals and fractions.


Worked Example

Example 1

Evaluate: If $x=3$x=3, evaluate $6x-4$6x4.

Think: This means that everywhere the letter $x$x has been written, we will replace it with the number $3$3.


$6x-4$6x4 $=$= $6\times3-4$6×34
  $=$= $18-4$184
  $=$= $14$14


The same process applies even if there is more than one unknown value.

Evaluate: If $x=6$x=6 and $y=0.5$y=0.5, evaluate $6x-2y-12$6x2y12.

Think: Just like before, we will replace the letter $x$x with the number $6$6, and the letter $y$y with the number $0.5$0.5. We also need to keep the order of operations in mind when we do these kinds of calculations!


$6x-2y-12$6x2y12 $=$= $6\times6-2\times0.5-12$6×62×0.512 replacing $x$x with $6$6, and $y$y with $0.5$0.5.
  $=$= $36-1-12$36112 evaluating multiplication before subtraction.
  $=$= $23$23  


Now let's watch some worked solutions to the following questions. 

Practice Questions

Question 1  

Evaluate $8x+4$8x+4 when $x=2$x=2.


Question 2

For  $x=10$x=10 and  $y=6$y=6, evaluate $8x+6y+4$8x+6y+4


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