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S1 Algebra: signs and inverse operations

1. Short teaching videos

1. 3 Minute Maths - Substitution — Whole short lesson. Focus on negative values, brackets and signs.

2. 1st Class Maths: Linear Equations (2 step/Brackets) — 2:20–5:16 (2m56s)

3. Cognito - How to Rearrange Formulas — Whole video, about 4:16.

2. Combined method and worked examples

Algebra substitution with negative numbers — method

Use brackets for negative values.

Worked example

a=5,b=-3: 2a-b=10-(-3)=13.

Solving linear equations with brackets — method

Expand the brackets first (multiply every term inside, watching negative signs), collect like terms, then use inverse operations on both sides. With letters on both sides, move the smaller x-term first. Check by substituting back.

Worked example

3(x-2)=2x+5 → 3x-6=2x+5 → x-6=5 → x=11. Check: 3(9)=27 and 2(11)+5=27 ✓.

Rearranging formulae — method

Undo operations on both sides.

Worked example

y=4x+9 -> x=(y-9)/4.

3. Practice — three questions per skill

Algebra substitution with negative numbers

Core practice · three questions

1. If a = −3 and b = 4, find 2a + b.
2. If x = −2, find 3x² − x.
3. If p = 5 and q = −3, find 4p − 3q.

Solving linear equations with brackets

Core practice · three questions

1. Solve 4(x + 3) = 28.
2. Solve 5(2x − 1) = 3x + 16.
3. Solve 3(x − 4) = 2(x + 1).

Rearranging formulae

Core practice · three questions

1. Make x the subject of y = 3x − 7.
2. Make w the subject of A = lw.
3. Make a the subject of v = u + at.