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Solve \[ \frac{3x - 2}{4} = \frac{2x + 5}{3} = \frac{1 - x}{6} \] x = __ - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 2
Question 11
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Solve \[ \frac{3x - 2}{4} = \frac{2x + 5}{3} = \frac{1 - x}{6} \] x = __
Worked Solution & Example Answer:Solve \[ \frac{3x - 2}{4} = \frac{2x + 5}{3} = \frac{1 - x}{6} \] x = __ - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 2
Step 1
Write the equation with a common denominator
Answer
To solve the equation, start by finding a common denominator for the fractions on both sides. The common denominator for 4, 3, and 6 is 12. We can rewrite each term as follows:
[ \frac{3x - 2}{4} = \frac{3(3x - 2)}{12} = \frac{9x - 6}{12} ]
[ \frac{2x + 5}{3} = \frac{4(2x + 5)}{12} = \frac{8x + 20}{12} ]
[ \frac{1 - x}{6} = \frac{2(1 - x)}{12} = \frac{2 - 2x}{12} ]
Now we can set up the equation:
[ 9x - 6 = 8x + 20 = 2 - 2x ]
Step 2
Isolate and solve for x
Answer
From the first part of the equation:
[ 9x - 6 = 8x + 20 ]
Subtract (8x) from both sides:
[ 9x - 8x - 6 = 20 ]
This simplifies to:
[ x - 6 = 20 ]
Adding 6 to both sides gives:
[ x = 26 ]
Now from the second part of the equation:
[ 9x - 6 = 2 - 2x ]
Adding (2x) to both sides:
[ 9x + 2x - 6 = 2 ]
This simplifies to:
[ 11x - 6 = 2 ]
Adding 6 to both sides gives:
[ 11x = 8 ]
Now, dividing both sides by 11 yields:
[ x = \frac{8}{11} ]
Step 3