How many solutions does the following equation have? 3(y+41)=3y+123 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Distribute the 3: Distribute the 3 on the left side of the equation to both terms inside the parentheses. 3(y+41) = 3y + 123 3*y + 3*41 = 3y + 123 3y + 123 = 3y + 123Observe both sides: Observe both sides of the equation to determine if they are identical. Since 3y + 123 is equal to 3y + 123, the equation is true for all values of y.Conclude the number of solutions: Conclude the number of solutions based on the observation in Step 2. Because the equation is true for all values of y, the equation has infinitely many solutions.

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How many solutions does the following equation have?

3(y+41)=3y+123
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $3(y+41)=3y+123$ $\newline$ 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

3(y+41)=3y+123

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $3$ : Distribute the $3$ on the left side of the equation to both terms inside the parentheses. $\newline$ $3(y+41) = 3y + 123$ $\newline$ $3\cdot y + 3\cdot 41 = 3y + 123$ $\newline$ $3y + 123 = 3y + 123$
Observe both sides: Observe both sides of the equation to determine if they are identical. $\newline$ Since $3y + 123$ is equal to $3y + 123$ , the equation is true for all values of $y$ .
Conclude the number of solutions: Conclude the number of solutions based on the observation in Step $2$ . $\newline$ Because the equation is true for all values of $y$ , the equation has infinitely many solutions.