# Substitute into algebraic add/sub expressions

Lesson

## Making the change

We've seen how we can use expressions, or rules, to take into account different situations. When we worked with positive numbers, we could swap our variable for number, in problems that involved addition and subtraction.

Here's an example of what we might use this for. Your cousin has to update the fuel prices on the big sign at the petrol station. He is given an expression that helps him work out how much premium fuel will cost, if he knows the price of standard fuel.

### negative numbers

Even if we need to substitute our variable with a negative number, we don't need to change how we do things. We simply change our variable for our number, and solve the number problem. We do need to remember the rules around working with negative numbers though:

• adding (+) a negative number (-) is the same as subtracting(-) a positive number
• subtracting (-) a negative number (-) is the same as adding (+) a positive number

Working with decimals or fractions doesn't change anything either, we use the same method of substitution. Your cousin has to deal with both of these scenarios in Video 2, so see how he handles it.

### hanging my pictures

For the final example, this video shows you how I actually used an expression with variables, like the ones we've been working on, to hang some pictures on my wall. Video 3 includes a little movie where I show you the pictures, and what I needed to do to hang them so they were centred on my wall.

#### Worked Examples

##### Question 1

Find the value of $9+m$9+m when $m=3$m=3.

##### Question 2

Evaluate $c+7$c+7 if:

1. $c$c is equal to $4$4

2. $c$c is equal to $-8$8

##### Question 3

Find the value of $w+z+y$w+z+y if $w$w is $26$26, $z$z is $-27$27, and $y$y is $-39$39.

### Outcomes

#### NA4-7

Form and solve simple linear equations