Solve for y. {:[(y-1)/(3y+7)=(1)/(10)],[y=◻]:}

Solve the equation: First, we will solve the equation (y-1)/(3y+7) = 1/10 for y.Multiply by (3y+7): Multiply both sides of the equation by (3y+7) to eliminate the denominator. (3y+7) * (y-1)/(3y+7) = (3y+7) * (1/10)Simplify the equation: Simplify the equation by canceling out the (3y+7) on the left side. y - 1 = (3y + 7)/10Multiply by 10: Multiply both sides by 10 to eliminate the fraction on the right side. 10(y - 1) = 3y + 7Distribute the 10: Distribute the 10 on the left side. 10y - 10 = 3y + 7Subtract 3y: Subtract 3y from both sides to get all y terms on one side. 10y - 10 - 3y = 3y + 7 - 3yCombine like terms: Combine like terms. 7y - 10 = 7Add 10: Add 10 to both sides to isolate the y term. 7y - 10 + 10 = 7 + 10Simplify the equation: Simplify the equation. 7y = 17Divide by 7: Divide both sides by 7 to solve for y. y = 17/7

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Math Problems

Algebra 1

Solve advanced linear inequalities

Full solution

Q. Solve for

y

\newline

\begin{array}{l} \frac{y-1}{3 y+7}=\frac{1}{10} \\ y=\square \end{array}

Solve the equation: First, we will solve the equation $(y-1)/(3y+7) = 1/10$ for $y$ .
Multiply by $(3y+7)$ : Multiply both sides of the equation by $(3y+7)$ to eliminate the denominator. $\newline$ $(3y+7) \cdot \frac{y-1}{3y+7} = (3y+7) \cdot \frac{1}{10}$
Simplify the equation: Simplify the equation by canceling out the $(3y+7)$ on the left side. $\newline$ $y - 1 = \frac{3y + 7}{10}$
Multiply by $10$ : Multiply both sides by $10$ to eliminate the fraction on the right side. $\newline$ $10(y - 1) = 3y + 7$
Distribute the $10$ : Distribute the $10$ on the left side. $10y - 10 = 3y + 7$
Subtract $3y$ : Subtract $3y$ from both sides to get all $y$ terms on one side. $\newline$ $10y - 10 - 3y = 3y + 7 - 3y$
Combine like terms: Combine like terms. $7y - 10 = 7$
Add $10$ : Add $10$ to both sides to isolate the $y$ term. $\newline$ $7y - 10 + 10 = 7 + 10$
Simplify the equation: Simplify the equation. $7y = 17$
Divide by $7$ : Divide both sides by $7$ to solve for $y$ . $y = \frac{17}{7}$