2.06 Substitution
We've seen how to substitute numerical values for pronumerals before. We follow the same process when the numerical values are negative.
Worked Example
Evaluate $7x-5$7x−5 when $x=6$x=6 and also when $x=-6$x=−6.
Think: There are two different values of $x$x, so we should substitute and then evaluate them individually.
Do: Let's substitute $x=6$x=6 first.
| $7x-5$7x−5 | $=$= | $7\times6-5$7×6−5 |
Substitute $x=6$x=6. |
| $=$= | $42-5$42−5 |
Evaluate the multiplication |
|
| $=$= | $37$37 |
Evaluate the subtraction |
Now let's substitute $x=-6$x=−6.
| $7x-5$7x−5 | $=$= | $7\times\left(-6\right)-5$7×(−6)−5 |
Substitute $x=-6$x=−6. |
| $=$= | $-42-5$−42−5 |
Evaluate the multiplication |
|
| $=$= | $-47$−47 |
Evaluate the subtraction |
Reflect: Notice that the values of $x$x are the negatives of each other, but the values of the expression are not. It is important that when we substitute values, the value that we substitute fits into exactly the same position as the pronumeral, and that we follow the order of operations.
Practice questions
Question 1
Find the value of $m+n$m+n when $m=6$m=6 and $n=-4$n=−4.
Question 2
Find the value of $\frac{p}{2q}$p2q when $p=-28$p=−28 and $q=-7$q=−7.
Question 3
Find the value of $k^2$k2 when $k=-7$k=−7.