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Solving Linear Equations involving Brackets
Mathematics Solving Linear Equations involving Brackets
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Aims of the Lesson The aim of this powerpoint is to help you…
Revise expanding brackets Solve simple linear equations that involve brackets.
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Equations with Brackets
There are two ways of solving equations involving brackets… EITHER expand the brackets first then re-arrange the equation collecting like terms together etc. before solving as you would a typical linear equation OR if appropriate, dividing through by what’s outside the brackets and then solving the linear equation remaining
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Revising Expanding Brackets
EACH item inside the brackets is multiplied by the value/term outside of the brackets… 5 ( x + y ) 5x + 5y 3 (2 + a) a – 7 (2b + 5) – 14b –35 – 2x (x – 7) – 2x2 + 14x
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Solving by Expanding First
Solve… 6 (3p + 2) = 84 Expanding gives… 18p + 12 = 84 Take 12 off both sides… 18p = Divide both sides by 18… p = Solve… 2 (x + 3) – 5x = 24 Expanding gives… 2x – 5x = 24 Simplifying gives… – 3x = 24 Take 6 off both sides… – 3x = 18 Divide both sides by – 3… x = – 6
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Solving by Dividing First
IF dividing does not bring up fractions immediately then divide first BUT don’t forget EVERY term needs to be divided throughout the equation…
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Examples 2 Solve… 8 (p – 5) = 48 Divide everything by 8… (p – 5) = 6
Add 5 to both sides… p = 11 Solve… 5(3 + r) – 20 = 75 Divide everything by 5… (3 + r) – 4 = 15 3 + r – 4 = 15 Simplify… r – 1 = 15 Add 1 to both sides… r = 16
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Beware… Answers can be negative or fractional
Don’t forget when dividing by a number you could simply write it as the bottom of a fraction… E.g. 12p = 5 Divide both sides by 12… p = 5/12
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What next? Make appropriate notes (including examples) on solving linear equations involving brackets or printout the prepared notes & complete the tasks within them. Work through the MyMaths lesson (and then its online homework) called: Algebra > Equations Linear > Equations 4 – Brackets Save and complete the worksheet: LinEq-S3.xlsx
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