Chapter 5: Linear equations

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Formula: y=3x+5
Equation: 7 = 3x + 5
What is the difference?

Formula: y=3x+5
What is the Slope?

Solve:
3 + 5x = 43

Solve:
Nisje = 14

Vocab: Terms

Terms are the parts of a formula that are added together or that are subtracted from each other.
In the formula 24 - 3t = h, the terms are 24 and -3t.
In the formula y = 2a + 8, the terms are 2a and 8.
In the formula p = 4 - 2t + 3 + 5t, the terms are 4, -2t, 3 and 5t

How many terms are there in this formula?
p = 8a + 4 - 2a

1. 1
2. 2
3. 3
4. 4

Solve:
5(x -1) -3x = 3(x -5)

Solve:

Solve

Solve:
(x +2)(x -5) = (x +1)sq -10

Vocab: Variables

In a linear formula there is a relation between two variables. They are the words (or letters if the formula is shortened) that can have a different value.
In the formula 20 + 5 x time in hours = amount in euro's, the variables are time and amount. (Remember from CH3: the units are hours and euro's)
In the formula p = 10a + 8 - 2a, the variables are p and a.

What are the variables in this formula?
t = 3a + 7 + 4a - 2

1. t, 3a and 4a
2. t and a
3. t, a and a
4. 3a, 7, 4a and -2

Vocab: Like terms

If there are several terms in a formula, we can call some of them like terms if they are the same type of term. This happens if they have the same variable.

In the formula a = 8c + 3 - 2c + 5,
8c and -2c are a pair of like terms and 3 and 5 are a pair of like terms.

In the formula p = 3a - 12 + 2b + 4a + 3b + 8,
3a and 4a are a pair of like terms, 2b and 3b are a pair of like terms, and -12 and 8 are a pair of like terms.

Simplifying formulas

When you add up the same number several times, you can write this as a multiplication.
In the same way, if you add up the same variable several times, you can write this as a mulitplication, which you can shorten.

Simplifying formulas

When you have like terms, you can add/subtract them.

Simplyfing formulas

When a formula contains several different like terms, you can shorten the formula by combining each type of like term.

Shorten the formula
a = 3t + 8 + 5t - 10

Notation

When formulas are shortened and you end up with a term such as 1t or -1c, you write this as t or -c.

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