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10+7x=4x+2+bx
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) 5
(C) 6
(D) 7

$10+7 x=4 x+2+b x$ $\newline$ In the equation shown, $b$ is a constant. For what value of $b$ does the equation have no solutions? $\newline$ Choose $1$ answer: $\newline$ (A) $3$ $\newline$ (B) $5$ $\newline$ (C) $6$ $\newline$ (D) $7$

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Find the constant of variation

Full solution

Q.

10+7 x=4 x+2+b x

\newline

In the equation shown,

b

is a constant. For what value of

b

does the equation have no solutions?

\newline

Choose

1

answer:

\newline

(A)

3

\newline

(B)

5

\newline

(C)

6

\newline

(D)

7

Move terms, simplify equation: First, let's simplify the equation by moving all terms involving $x$ to one side and constants to the other side. We subtract $4x$ from both sides to get $10 + 7x - 4x = 2 + bx$ .
Simplify left side: Simplifying the left side, we get $10 + 3x = 2 + bx$ .
Find value of b: Now, we want to find the value of b for which the equation has no solutions. This will happen when the coefficients of x on both sides are equal, and the constants are not equal, which would make the equation inconsistent. So we set $3$ equal to $b$ and $10$ not equal to $2$ .
Equation with no solutions: Since we want no solutions, we have $b = 3$ and $10 \neq 2$ . This means that when $b$ is $3$ , the equation becomes $10 + 3x = 2 + 3x$ , which simplifies to $10 \neq 2$ , an inequality that is always true. Therefore, the equation has no solutions when $b = 3$ .

More problems from Find the constant of variation

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Question

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\newline

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Question

Which equation describes this relationship? Remember to include

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d

\newline

\newline

\[[A]a = \frac{kb}{cd}\]

\newline

\[[B]a = \frac{kbd}{c}\]

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\[[C]a = \frac{k}{bcd}\]

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\newline

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