Free examples and worked answers. No account needed.
Practise the method.
Brackets, fractions and deeper modelling
12 equations and worded problems. 20 minutes; feedback at the end.
Example 1
5(x+7)−10=20
Show worked answer
Answer: −1
Add 10 and divide by 5:x+7=6.
Subtract 7:x=−1.
Substitution gives 20 on both sides.
Example 2
Taxi A charges $5.00 plus $1.25 per kilometre. Taxi B charges $33.50 plus $0.50 per kilometre. For what distance, in kilometres, do they cost the same?
Show worked answer
Answer: 38
Let x be the distance in kilometres.
5.00+1.25x=33.50+0.50x.
Subtract the lower rate and the first fee: 0.75x=28.50.
So x=38km;
both fares are $52.50.
Example 3
7(x+11)=5(x−3)+124
Show worked answer
Answer: 16
Expand and collect: 2x=32.
Divide by 2:x=16.
Both sides equal 189 after substitution.
Put it into practice.
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