How many solutions does the following equation have? 3(y+9)=12 y+13 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 y and 9. 3(y+9) = 3*y + 3*9 = 3y + 27Rewrite the equation: Rewrite the equation with the distributed terms. 3y + 27 = 12y + 13Move terms involving y: Move all terms involving y to one side of the equation and constants to the other side. Subtract 3y from both sides: 3y + 27 - 3y = 12y + 13 - 3y 27 = 9y + 13Subtract 13: Subtract 13 from both sides to isolate the term with y. 27 - 13 = 9y + 13 - 13 14 = 9yDivide both sides: Divide both sides by 9 to solve for y. 14 / 9 = 9y / 9 y = 14 / 9Check the solution: Check if the solution is valid by substituting y back into the original equation. 3((14/9)+9) = 12*(14/9)+13 3(14/9+81/9) = 168/9+13 3(95/9) = 168/9+117/9 285/9 = 285/9

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How many solutions does the following equation have?

3(y+9)=12 y+13
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $3(y+9)=12y+13$ $\newline$ 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+9)=12y+13

\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 $y$ and $9$ .
$3(y+9) = 3\cdot y + 3\cdot 9$
= $3y + 27$
Rewrite the equation: Rewrite the equation with the distributed terms. $3y + 27 = 12y + 13$
Move terms involving $y$ : Move all terms involving $y$ to one side of the equation and constants to the other side. $\newline$ Subtract $3y$ from both sides: $\newline$ $3y + 27 - 3y = 12y + 13 - 3y$ $\newline$ $27 = 9y + 13$
Subtract $13$ : Subtract $13$ from both sides to isolate the term with $y$ . $\newline$ $27 - 13 = 9y + 13 - 13$ $\newline$ $14 = 9y$
Divide both sides: Divide both sides by $9$ to solve for $y$ . $\newline$ $\frac{14}{9} = \frac{9y}{9}$ $\newline$ $y = \frac{14}{9}$
Check the solution: Check if the solution is valid by substituting $y$ back into the original equation. $3\left(\frac{14}{9}+9\right) = 12\times\frac{14}{9}+13$ $3\left(\frac{14}{9}+\frac{81}{9}\right) = \frac{168}{9}+13$ $3\left(\frac{95}{9}\right) = \frac{168}{9}+\frac{117}{9}$ $\frac{285}{9} = \frac{285}{9}$