Algebraic expressions

Variables, coefficients, like terms, substitution, formulae and word formulae. Read one part at a time and tap “I know this”. Then test yourself in the quiz.

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The language of algebra

Term	Meaning	In 3x + 5
variable	a letter for an unknown number	x
coefficient	the number in front of the variable	3
constant	a number without a letter	5
term	parts separated by + or −	3x and 5

3x means 3 × x.
Like terms have the same letter and can be added: 4a + 2a = 6a. But 4a + 2b stays as it is.

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Substitution and formulae

Substitute the number for the letter: if x = 4, then 3x + 5 = 3 × 4 + 5 = 17. With integers: x = −2 → 3 × (−2) + 5 = −1.

A formula is a rule with letters: perimeter of a square P = 4s. If s = 6 cm, P = 24 cm.

A word formula gives the rule in words: cost of a taxi trip = R15 plus R8 for every km. With letters: C = 15 + 8k. For 12 km: C = 15 + 8 × 12 = R111.

Rule

A number sentence from words: “I think of a number, multiply it by 4 and add 3; the answer is 31.” → 4 × □ + 3 = 31, so □ = 7 (31 − 3 = 28; 28 ÷ 4 = 7).

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Remember this: your summary

A variable is a letter for an unknown.
3x = 3 × x; 3 is the coefficient.
Only like terms can be added.
Substitute the number and calculate.
A formula is a rule with letters; a word formula gives it in words.

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Memory trick

Apples with apples: 4a + 2a = 6a, but apples and bananas (a and b) stay apart.

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Important words

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Test yourself · Part 2

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