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Find the value of \( \frac{2n+1}{3n-2} \) when \( n = 4 \) - Junior Cycle Mathematics - Question 8 - 2017
Question 8
Find the value of \( \frac{2n+1}{3n-2} \) when \( n = 4 \). Multiply out and simplify \( (w + 4)(3w - 2) \).
Worked Solution & Example Answer:Find the value of \( \frac{2n+1}{3n-2} \) when \( n = 4 \) - Junior Cycle Mathematics - Question 8 - 2017
Step 1
Find the value of \( \frac{2n+1}{3n-2} \) when \( n = 4 \)
Answer
To find the value of ( \frac{2n+1}{3n-2} ) when ( n = 4 ), substitute ( n = 4 ) into the expression:
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Calculate the numerator: [ 2(4) + 1 = 8 + 1 = 9 ]
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Calculate the denominator: [ 3(4) - 2 = 12 - 2 = 10 ]
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Now, substitute these values into the fraction: [ \frac{9}{10} ]
Thus, the answer is ( \frac{9}{10} ).
Step 2
Multiply out and simplify \( (w + 4)(3w - 2) \)
Answer
Using the distributive property (also known as the FOIL method for binomials):
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Multiply the first terms: [ w \cdot 3w = 3w^2 ]
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Multiply the outer terms: [ w \cdot (-2) = -2w ]
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Multiply the inner terms: [ 4 \cdot 3w = 12w ]
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Multiply the last terms: [ 4 \cdot (-2) = -8 ]
Now, combine all these results: [ 3w^2 + 12w - 2w - 8 = 3w^2 + 10w - 8 ]
Thus, the simplified expression is ( 3w^2 + 10w - 8 ).