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How many solutions does the following equation have?

-9(x+6)=-9x+108
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-9(x+6)=-9x+108$ $\newline$ 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

-9(x+6)=-9x+108

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

(C) Infinitely many solutions

Distribute $-9$ to both terms: Distribute $-9$ to both terms inside the parentheses. $-9(x+6) = -9x - 9 \times 6$ $= -9x - 54$
Write equation with distributed terms: Write the equation with the distributed terms. $\newline$ $-9x - 54 = -9x + 108$
Isolate variable x by adding $9$ x: Attempt to isolate the variable x on one side by adding $9x$ to both sides of the equation. $\newline$ $-9x + 9x - 54 = -9x + 9x + 108$ $\newline$ $0 - 54 = 108$
Simplify both sides of equation: Simplify both sides of the equation. $\newline$ $-54 = 108$ $\newline$ This is a false statement, indicating that there is no value of $x$ that can satisfy the equation.
Conclude number of solutions: Conclude the number of solutions based on the previous step. $\newline$ Since $-54$ does not equal $108$ , there are no values of $x$ that can make the equation true. Therefore, the equation has no solutions.

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