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How many solutions does the following equation have?

-4x-7+10 x=-7+6x
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-4x-7+10x=-7+6x$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

-4x-7+10x=-7+6x

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

(C) Infinitely many solutions

Combine like terms: Combine like terms on both sides of the equation. $\newline$ $-4x - 7 + 10x = -7 + 6x$ $\newline$ Combine the x terms on the left side: $-4x + 10x = 6x$ $\newline$ Combine the constant terms on the left side: $-7 = -7$ $\newline$ So the equation simplifies to: $\newline$ $6x = -7 + 6x$
Combine $x$ terms: Subtract $6x$ from both sides of the equation to move all $x$ terms to one side. $\newline$ $6x - 6x = -7 + 6x - 6x$ $\newline$ This simplifies to: $\newline$ $0 = -7$
Combine constant terms: Analyze the simplified equation. $\newline$ $0 = -7$ is a false statement, which means there is no value of $x$ that can satisfy the equation.

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