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

To find the values of c and d, we first simplify the equation:

1. Expand the left side:

   $5(2(x + 1)) = 10x + 5$

   So, the equation becomes:

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

2. Rearranging gives:

   $c(x + d) = 12x - 1 - 10x - 5$ $c(x + d) = 2x - 6$

3. Now, we will compare coefficients for x:

   We have:

   • Coefficient of x: 2 = c

   Thus, we find:

   • $c = 2$

4. Next, equate the constant terms:

   We know from our expansion that:

   $cd = -6$

5. Since we know that:

   • $c = 2$

   Therefore:

   • Substituting gives: $2d = -6$
   • Solve for d:

   $d = -3$

Combining these results, we have:

• $c = 2$
• $d = -3$