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$Solve for y. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -65 y+19 < -2y+41$

Solve for $y$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ -65y + 19 < -2y + 41

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Solve multi-step inequalities

Full solution

Q. Solve for

y

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

\newline

-65y + 19 < -2y + 41

Isolate variable y: Isolate the variable y on one side of the inequality by moving the terms involving y to one side and the constant terms to the other side. $\newline$ -65y + 19 < -2y + 41 $\newline$ Add $65y$ to both sides to move the y terms to one side: $\newline$ -65y + 65y + 19 < -2y + 65y + 41 $\newline$ Simplify: $\newline$ 19 < 63y + 41
Move constant terms: Now, isolate the constant terms on the other side by subtracting $41$ from both sides: $\newline$ 19 - 41 < 63y + 41 - 41 $\newline$ Simplify: $\newline$ -22 < 63y
Divide both sides: Divide both sides by $63$ to solve for y: $\newline$ (-22)/63 < 63y/63 $\newline$ Simplify: $\newline$ -22/63 < y $\newline$ Reduce the fraction $-22/63$ to its lowest terms: $\newline$ $-22/63 = -2/9$ (since both $22$ and $63$ are divisible by $11$ )
Final reduced inequality: The final inequality in the reduced form is: $\newline$ -\frac{2}{9} < y $\newline$ This means $y$ is greater than $-\frac{2}{9}$ .

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