Solve the inequality and express the solution set using interval notation. $10 ( x + 2 ) - 5 ( x - 7 )

Question

Solve the inequality and express the solution set using interval notation. $10 ( x + 2 ) - 5 ( x - 7 ) < 0$
A) $( - 11 , + \infty )$
B) $( - \infty , - 11 )$
C) $( - \infty , - 11 ]$
D) $[ - 11 , + \infty )$

Quizplus · Accepted Answer

First, simplify the inequality: $10(x + 2) - 5(x - 7) = 10x + 20 - 5x + 35 = 5x + 55 < 0$. Solving for $x$, we get $5x < -55$, so $x < -11$. This means the solution set is all values less than -11, which is represented by $(-\infty, -11)$.

Solve the Inequality and Express the Solution Set Using Interval 10(x+2)−5(x−7)<010 ( x + 2 ) - 5 ( x - 7 ) < 010(x+2)−5(x−7)<0

Solve the Inequality and Express the Solution Set Using Interval $10 ( x + 2 ) - 5 ( x - 7 ) < 0$