How many solutions does the following equation have? 7(y+3)=5y+8 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

Distribute the 7: Distribute the 7 to both terms inside the parentheses. 7(y+3) = 7*y + 7*3 = 7y + 21Rewrite the equation: Rewrite the equation with the distributed terms. 7y + 21 = 5y + 8Move terms with y: Move all terms containing y to one side of the equation by subtracting 5y from both sides. 7y + 21 - 5y = 5y + 8 - 5y = 2y + 21 = 8Move constant term: Move the constant term on the y-side to the other side by subtracting 21 from both sides. 2y + 21 - 21 = 8 - 21 = 2y = -13Solve for y: Solve for y by dividing both sides by 2. 2y/2 = -13/2 = y = -6.5

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How many solutions does the following equation have?

7(y+3)=5y+8
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $7(y+3)=5y+8$ $\newline$ 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

7(y+3)=5y+8

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $7$ : Distribute the $7$ to both terms inside the parentheses. $\newline$ $7(y+3) = 7\cdot y + 7\cdot 3$ $\newline$ $= 7y + 21$
Rewrite the equation: Rewrite the equation with the distributed terms. $7y + 21 = 5y + 8$
Move terms with $y$ : Move all terms containing $y$ to one side of the equation by subtracting $5y$ from both sides. $\newline$ $7y + 21 - 5y = 5y + 8 - 5y$ $\newline$ $= 2y + 21 = 8$
Move constant term: Move the constant term on the y-side to the other side by subtracting $21$ from both sides. $\newline$ $2y + 21 - 21 = 8 - 21$ $\newline$ $= 2y = -13$
Solve for y: Solve for y by dividing both sides by $2$ . $\newline$ $\frac{2y}{2} = \frac{-13}{2}$ $\newline$ $\Rightarrow y = -6.5$