Topic 4 of 11 · Form 2
Equations and inequalities
Collect like terms and use inverse operations; equations with fractions (multiply through by the LCM).
Notes for this topic 1 file, in order
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Linear equations
Collect like terms and use inverse operations; equations with fractions (multiply through by the LCM).
Simultaneous equations
By elimination or substitution; one linear and one quadratic by substitution.
Worked example: Solve 3x + 2y = 16 and x − y = 2.
x = y + 2 → 3y + 6 + 2y = 16 → y = 2, x = 4
Quadratic equations
By factorising, completing the square or the formula x = [−b ± √(b² − 4ac)]/2a.
Worked example: Solve 2x² − 3x − 4 = 0, giving answers to 2 decimal places.
x = [3 ± √(9 + 32)]/4 = (3 ± 6.403)/4 → x = 2.35 or x = −0.85
Inequalities
Solve like equations, but reverse the sign when multiplying or dividing by a negative number. Represent on a number line; find integer solutions; regions on graphs (shade unwanted regions as instructed).
Worked example: Solve 5 − 2x < 11.
−2x < 6 → x > −3
Forming equations
Translate word problems into equations, solve, and check that the answer makes sense.
Check yourself
- Solve 4(x − 3) = 2x + 6.
- Solve x² − 5x − 14 = 0.
- List the integers satisfying −2 ≤ x < 3.
Show answers
- x = 9
- (x − 7)(x + 2) = 0 → x = 7 or x = −2
- −2, −1, 0, 1, 2
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