−4+bx=2x+3(x+1) in the equation shown above, b is a constant. for what value of b does the equation have no solutions?

b=5

Step-by-step explanation:

−4+bx=2x+3(x+1)  (expand parenthesis first, i.e PEDMAS)

−4 + bx = 2x + 3x + 3

−4 + bx = 5x + 3   (move all x terms to one side and constants to another)

5x - bx = - 4 -3

5x - bx = - 7  (factor out x)

(5 - b)x = - 7

x = -7 / (5-b)

we can see that 5-b is in the denominator. Recall that for a fraction, the denominator cannot be zero otherwise the expression is undefined. (i.e no solutions)

hence the  expression is undefined if,

(5-b) = 0

or b = 5

answer for #1 is c

answer for #2 is d

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