-4+bx=2x+3(x+1) In the equation shown, b is a constant. For what value of b does the equation have no solutions? Choose 1 answer: (A) 3 (B) 4 (c) 5 (D) 6

Distribute and Simplify: First, we need to simplify the right side of the equation by distributing the 3 into the parentheses. Calculation: 2x + 3(x + 1) = 2x + 3x + 3 Simplified: 2x + 3x + 3 = 5x + 3Rearrange Terms: Next, we want to bring all terms involving x to one side of the equation and constants to the other side to compare the coefficients of x. Calculation: -4 + bx = 5x + 3 Rearrange: bx - 5x = 3 + 4 Simplified: (b - 5)x = 7Find Coefficient of x: For the equation to have no solutions, the coefficient of x on both sides must be different, and the constants must be the same. Since there is no constant on the left side, we need the coefficient of x to be zero. Calculation: b - 5 = 0 Solve for b: b = 5Determine No Solutions: We have found the value of b that makes the coefficient of x on both sides of the equation equal, which would normally mean the equation has infinitely many solutions. However, since the constants are different (7 on the right side and none on the left), the equation has no solutions.

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-4+bx=2x+3(x+1)
In the equation shown,
b is a constant. For what value of
b does the equation have no solutions?
Choose 1 answer:
(A) 3
(B) 4
(c) 5
(D) 6

$-4+bx=2x+3(x+1)$ $\newline$ In the equation shown, $\newline$ $b$ is a constant. For what value of $\newline$ $b$ does the equation have no solutions? $\newline$ Choose $1$ answer: $\newline$ (A) $3$ $\newline$ (B) $4$ $\newline$ (C) $5$ $\newline$ (D) $6$

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Full solution

-4+bx=2x+3(x+1)

\newline

In the equation shown,

\newline

b

is a constant. For what value of

\newline

b

does the equation have no solutions?

\newline

Choose

1

answer:

\newline

(A)

3

\newline

(B)

4

\newline

(C)

5

\newline

(D)

6

Distribute and Simplify: First, we need to simplify the right side of the equation by distributing the $3$ into the parentheses. $\newline$ Calculation: $2x + 3(x + 1) = 2x + 3x + 3$ $\newline$ Simplified: $2x + 3x + 3 = 5x + 3$
Rearrange Terms: Next, we want to bring all terms involving $x$ to one side of the equation and constants to the other side to compare the coefficients of $x$ .
Calculation: $-4 + bx = 5x + 3$
Rearrange: $bx - 5x = 3 + 4$
Simplified: $(b - 5)x = 7$
Find Coefficient of $x$ : For the equation to have no solutions, the coefficient of $x$ on both sides must be different, and the constants must be the same. Since there is no constant on the left side, we need the coefficient of $x$ to be zero. $\newline$ Calculation: $b - 5 = 0$ $\newline$ Solve for $b$ : $b = 5$
Determine No Solutions: We have found the value of $b$ that makes the coefficient of $x$ on both sides of the equation equal, which would normally mean the equation has infinitely many solutions. However, since the constants are different ( $7$ on the right side and none on the left), the equation has no solutions.