(2)/(3)-5x=bx+(1)/(3) In the equation shown, b is a constant. For what value of b does the equation have no solutions? Choose 1 answer: (A) 5 (B) 0 (C) -5 (D) (2)/(3)

Isolate variable x: We start by trying to isolate the variable x on one side of the equation to see if we can solve for x in terms of b. (2/3) - 5x = bx + (1/3)Subtract constants: Subtract (1/3) from both sides to get the x terms on one side and the constants on the other. (2/3) - (1/3) - 5x = bxCombine constants: Combine the constants on the left side. (1/3) - 5x = bxAdd x terms: Add 5x to both sides to get all the x terms on one side. (1/3) = bx + 5xFactor out x: Factor out x on the right side. (1/3) = x(b + 5)Set coefficient to zero: For the equation to have no solutions, the right side must never equal the left side for any value of x. This can only happen if the coefficient of x on the right side is zero, because any non-zero number times x could potentially equal (1/3). So, we set the coefficient of x to zero. b + 5 = 0Solve for b: Subtract 5 from both sides to solve for b. b = -5

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(2)/(3)-5x=bx+(1)/(3)
In the equation shown,
b is a constant. For what value of
b does the equation have no solutions?
Choose 1 answer:
(A) 5
(B) 0
(C) -5
(D)
(2)/(3)

$\frac{2}{3}-5x=bx+\frac{1}{3}$ $\newline$ 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) $5$ $\newline$ (B) $0$ $\newline$ (C) $-5$ $\newline$ (D) $\frac{2}{3}$

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Full solution

\frac{2}{3}-5x=bx+\frac{1}{3}

\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)

5

\newline

(B)

0

\newline

(C)

-5

\newline

(D)

\frac{2}{3}

Isolate variable x: We start by trying to isolate the variable x on one side of the equation to see if we can solve for x in terms of b. $\newline$ $\frac{2}{3} - 5x = bx + \frac{1}{3}$
Subtract constants: Subtract $(\frac{1}{3})$ from both sides to get the x terms on one side and the constants on the other. $\newline$ $(\frac{2}{3}) - (\frac{1}{3}) - 5x = bx$
Combine constants: Combine the constants on the left side. $\newline$ $(\frac{1}{3}) - 5x = bx$
Add $x$ terms: Add $5x$ to both sides to get all the $x$ terms on one side. $\newline$ $\frac{1}{3} = bx + 5x$
Factor out x: Factor out x on the right side. $\newline$ $\frac{1}{3} = x(b + 5)$
Set coefficient to zero: For the equation to have no solutions, the right side must never equal the left side for any value of $x$ . This can only happen if the coefficient of $x$ on the right side is zero, because any non-zero number times $x$ could potentially equal $(\frac{1}{3})$ . So, we set the coefficient of $x$ to zero. $b + 5 = 0$
Solve for $b$ : Subtract $5$ from both sides to solve for $b$ . $b = -5$