Worked Solution & Example Answer:Solve
$$\frac{3x - 2}{4} = \frac{2x + 5}{3} = \frac{1 - x}{6}$$ - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 2
Step 1
Find a Common Denominator
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Answer
To solve the equation, we first need to eliminate the fractions by finding a common denominator. The denominators are 4, 3, and 6. The least common denominator (LCD) is 12.
We will multiply each term by 12:
12×43x−2=12×32x+5=12×61−x
Step 2
Expand the Equation
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Answer
This gives us:
For the first term:
12×43x−2=3(3x−2)=9x−6
For the second term:
12×32x+5=4(2x+5)=8x+20
For the third term:
12×61−x=2(1−x)=2−2x
Now we can rewrite the equation as:
9x−6=8x+20=2−2x
Step 3
Set Up the Two Equations
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Answer
We can now set up two separate equations to solve:
From the first part:
9x−6=8x+20
From the second part:
8x+20=2−2x
Step 4
Solve Each Equation
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Answer
Solving the first equation:
9x−8x=20+6⇒x=26
Solving the second equation:
8x+2x=2−20⇒10x=−18⇒x=−1018=−59
Thus, we find two values: ( x = 26 ) and ( x = -\frac{9}{5} ).
