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10 (a) Solve \( \frac{9 + x}{7} = 11 - x \) \( x = \) (b) Simplify \( \frac{4(y + 3)^3}{(y + 3)^2} \) \( x = \) - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 3

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Question 11

10-(a)-Solve-\(-\frac{9-+-x}{7}-=-11---x-\)---\(-x-=-\)---(b)-Simplify-\(-\frac{4(y-+-3)^3}{(y-+-3)^2}-\)---\(-x-=-\)-Edexcel-GCSE Maths-Question 11-2019-Paper 3.png

10 (a) Solve \( \frac{9 + x}{7} = 11 - x \) \( x = \) (b) Simplify \( \frac{4(y + 3)^3}{(y + 3)^2} \) \( x = \)

Worked Solution & Example Answer:10 (a) Solve \( \frac{9 + x}{7} = 11 - x \) \( x = \) (b) Simplify \( \frac{4(y + 3)^3}{(y + 3)^2} \) \( x = \) - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 3

Step 1

Solve \( \frac{9 + x}{7} = 11 - x \)

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Answer

To solve the equation, first multiply both sides by 7:

[ 9 + x = 7(11 - x) ]

Distributing the right-hand side, we have:

[ 9 + x = 77 - 7x ]

Next, combine like terms by moving all terms involving ( x ) to one side and constants to the other:

[ x + 7x = 77 - 9 ]

This simplifies to:

[ 8x = 68 ]

Now, divide both sides by 8 to isolate ( x ):

[ x = \frac{68}{8} = 8.5 ]

Step 2

Simplify \( \frac{4(y + 3)^3}{(y + 3)^2} \)

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Answer

To simplify the expression, note that we can cancel out one ( (y + 3)^2 ) from the numerator and the denominator:

[ \frac{4(y + 3)^3}{(y + 3)^2} = 4(y + 3)^{3-2} = 4(y + 3) ]

Thus, the simplified expression is:

[ 4(y + 3) ]

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