Choose the one alternative that best completes the statement or answers the question.
Solve the inequality. Write the solution set in interval notation.
-$$- 2 ( 7 y - 7 ) + y 2 y - ( - 5 + y )$$
A) $\left( - \infty , \frac { 9 } { 14 } \right)$
B) $\left( \frac { 9 } { 14 } , \infty \right)$
C) $\left( \frac { 2 } { 7 } , \infty \right)$
D) $\left( - \infty , \frac { 9 } { 14 } \right]$

Question

Choose the one alternative that best completes the statement or answers the question.
Solve the inequality. Write the solution set in interval notation.
-$$- 2 ( 7 y - 7 ) + y > 2 y - ( - 5 + y )$$
A) $\left( - \infty , \frac { 9 } { 14 } \right)$
B) $\left( \frac { 9 } { 14 } , \infty \right)$
C) $\left( \frac { 2 } { 7 } , \infty \right)$
D) $\left( - \infty , \frac { 9 } { 14 } \right]$

Quizplus · Accepted Answer

First, simplify both sides of the inequality: $$-2(7y - 7) + y > 2y - (-5 + y)$$ becomes $$-14y + 14 + y > 2y + 5 - y$$. Simplifying further gives $$-13y + 14 > y + 5$$, which simplifies to $$-14y > -9$$, leading to $y < \frac{9}{14}$. Thus, the solution in interval notation is $\left( - \infty , \frac { 9 } { 14 } \right)$.

Choose the One Alternative That Best Completes the Statement or Answers