How many solutions does the following equation have? 4(y-30)=4y+12 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute the 4: Distribute the 4 on the left side of the equation to both terms inside the parentheses. 4(y-30) = 4y + 12 4*y - 4*30 = 4y + 12 4y - 120 = 4y + 12Attempt to isolate the variable: Attempt to isolate the variable y on one side of the equation by subtracting 4y from both sides. 4y - 120 - 4y = 4y + 12 - 4y 0 - 120 = 12 -120 = 12Analyze the resulting statement: Analyze the resulting statement. -120 = 12 is a false statement, which means there is no value of y that can satisfy the equation.Conclude the number of solutions: Conclude the number of solutions based on the analysis. Since the equation leads to a false statement, it means that there are no values of y that can make the equation true. Therefore, the equation has no solutions.

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How many solutions does the following equation have?

4(y-30)=4y+12
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $4(y-30)=4y+12$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

4(y-30)=4y+12

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $4$ : Distribute the $4$ on the left side of the equation to both terms inside the parentheses. $\newline$ $4(y-30) = 4y + 12$ $\newline$ $4\cdot y - 4\cdot 30 = 4y + 12$ $\newline$ $4y - 120 = 4y + 12$
Attempt to isolate the variable: Attempt to isolate the variable $y$ on one side of the equation by subtracting $4y$ from both sides. $\newline$ $4y - 120 - 4y = 4y + 12 - 4y$ $\newline$ $0 - 120 = 12$ $\newline$ $-120 = 12$
Analyze the resulting statement: Analyze the resulting statement. $\newline$ $-120 = 12$ is a false statement, which means there is no value of $y$ that can satisfy the equation.
Conclude the number of solutions: Conclude the number of solutions based on the analysis. $\newline$ Since the equation leads to a false statement, it means that there are no values of $y$ that can make the equation true. Therefore, the equation has no solutions.