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$Solve for y. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 5y+3 > -7y+13$

Solve for $y$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ 5y + 3 > -7y + 13

Full solution

Q. Solve for

y

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

5y + 3 > -7y + 13

Isolate y: First, we need to isolate the variable $y$ on one side of the inequality. To do this, we will add $7y$ to both sides of the inequality to move all the $y$ terms to the left side. $\newline$ 5y + 3 + 7y > -7y + 13 + 7y $\newline$ This simplifies to: $\newline$ 12y + 3 > 13
Add $7y$ : Next, we will subtract $3$ from both sides of the inequality to isolate the term with $y$ on the left side. $\newline$ 12y + 3 - 3 > 13 - 3 $\newline$ This simplifies to: $\newline$ 12y > 10
Subtract $3$ : Now, we will divide both sides of the inequality by $12$ to solve for $y$ . $\newline$ \frac{12y}{12} > \frac{10}{12} $\newline$ This simplifies to: $\newline$ y > \frac{10}{12}
Divide by $12$ : Finally, we will reduce the fraction $\frac{10}{12}$ to its lowest terms. $\newline$ $\frac{10}{12}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $10 \div 2 = 5$ $\newline$ $12 \div 2 = 6$ $\newline$ So, $\frac{10}{12}$ simplifies to $\frac{5}{6}$ . $\newline$ y > \frac{5}{6}