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Answer:
c = 4, d = - 1
Step-by-step explanation:
Expand and simplify left side, then compare coefficients of like terms on the right side, that is
3(2x + d) + c(x + 5) ← distribute parenthesis
6x + 3d + cx + 5c
= x(6 + c) + 3d + 5c
Compare terms with those on the right side
coefficients of x- terms
6 + c = 10 ( subtract 6 from both sides )
c = 4
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constant terms
3d + 5c = 17, that is
3d + 5(4) = 17
3d + 20 = 17 ( subtract 20 from both sides )
3d = - 3 ( divide both sides by 3 )
d = - 1
The value of c and d if 3(2x+d)+c(x+5)=10x+17 is 4 and -1 respectively
Given the equation:
3(2x+d)+c(x+5)=10x+17
Expand the bracket
6x + 3d + cx + 5c = 10x + 17
Collect the like terms
6x+cx + 3d + 5c = 10x + 17
x(6+c) + 3d + 5c = 10x + 17
Compare the coefficients of x on both sides
x(6+c) = 10x
6+c = 10
c = 10 - 6
c = 4
Similarly:
3d + 5c = 17
3d + 5(4) = 17
3d + 20 = 17
3d = 17 - 20
3d = -3
d =-3/3
d = -1
Hence the value of c and d if 3(2x+d)+c(x+5)=10x+17 is 4 and -1 respectively
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