GCSE OCR Maths Solving equations: 5(2(x + 1)) + c(x + d) = 12x

5(2(x + 1)) + c(x + d) = 12x - 1 Work out the value of c and the value of d. - OCR - GCSE Maths - Question 11 - 2020 - Paper 3

Question 11

5(2(x + 1)) + c(x + d) = 12x - 1 Work out the value of c and the value of d.

Worked Solution & Example Answer:5(2(x + 1)) + c(x + d) = 12x - 1 Work out the value of c and the value of d. - OCR - GCSE Maths - Question 11 - 2020 - Paper 3

Step 1

Step 1: Expand the equation

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Answer

Start by expanding the left side of the equation:

$5(2(x + 1)) + c(x + d) = 12x - 1$

This simplifies to:

$10x + 5 + cx + cd = 12x - 1$

Step 2

Step 2: Combine like terms

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Answer

Now, combine the terms involving $x$ :

$(10 + c)x + (5 + cd) = 12x - 1$

This gives us a system of equations by equating coefficients.

Step 3

Step 3: Set up the system of equations

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Answer

From the equation above, we can derive two equations:

For the coefficients of $x$ : $10 + c = 12$
For the constant terms: $5 + cd = -1$

Step 4

Step 4: Solve for c

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Answer

From the first equation, solve for $c$ :

$c = 12 - 10 = 2$

Step 5

Step 5: Solve for d

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Answer

Substituting $c = 2$ into the second equation:

$5 + 2d = -1$

Now, solve for $d$ :

$2d = -1 - 5 = -6 \\ d = \frac{-6}{2} = -3$

Step 6

Final values

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Answer

Thus, the values are:

$c = 2$
$d = -3$

5(2(x + 1)) + c(x + d) = 12x - 1 Work out the value of c and the value of d. - OCR - GCSE Maths - Question 11 - 2020 - Paper 3

Worked Solution & Example Answer:5(2(x + 1)) + c(x + d) = 12x - 1 Work out the value of c and the value of d. - OCR - GCSE Maths - Question 11 - 2020 - Paper 3

Step 1: Expand the equation

Step 2: Combine like terms

Step 3: Set up the system of equations

Step 4: Solve for c

Step 5: Solve for d

Final values

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