Question

2(c-6x)+d(5x-1)=2(4x+5) work out c and d

Answer 1

c = 7

d = 4

Explanation:

To determine the values of c and d in the given equation, expand the brackets and rearrange the terms:

`\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\2c-12x+5dx-d&=8x+10\\5dx-12x+2c-d&=8x+10\\(5d-12)x+(2c-d)&=8x+10\end{aligned}`

To solve for d, equate the terms in x:

`\begin{aligned}(5d-12)x&=8x\\5d-12&=8\\5d&=20\\d&=4\end{aligned}`

To solve for c, equate the constants and substitute the found value of d:

`\begin{aligned}2c-d&=10\\2c-4&=10\\2c&=14\\c&=7\end{aligned}`

Therefore, the values of c and d are:

• c = 7
• d = 4

Check by substituting the found values of c and d into the original equation:

`\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\\\c=7,\;d=4\implies 2(7-6x)+4(5x-1)&=2(4x+5)\\14-12x+20x-4&=8x+10\\20x-12x+14-4&=8x+10\\8x+10&=8x+10\end{aligned}`