3.05 Substitution

Lesson

We've seen how to substitute numerical values for variables before. We follow the same process when the numerical values are negative.

Worked example

Evaluate $7x-5$7x5 when $x=6.2$x=6.2 and also when $x=-6.2$x=6.2.

Think: There are two different values of $x$x, so we should substitute and then evaluate them individually.

Do: Let's substitute $x=6.2$x=6.2 first.

 $7x-5$7x−5 $=$= $7\times6.2-5$7×6.2−5 Substitute $x=6.2$x=6.2. $=$= $43.4-5$43.4−5 Evaluate the multiplication $=$= $38.4$38.4 Evaluate the subtraction

Now let's substitute $x=-6.2$x=6.2.

 $7x-5$7x−5 $=$= $7\times\left(-6.2\right)-5$7×(−6.2)−5 Substitute $x=-6.2$x=−6.2. $=$= $-43.4-5$−43.4−5 Evaluate the multiplication $=$= $-48.4$−48.4 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 variable, 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.

Outcomes

9.B3.4

Solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate.