Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7 1$ A) $( - \infty , - 4 ] \cup [ - 3 , \infty )$ B) $( - \infty , \infty )$ C) $( - \infty , - 3 ) \cup ( - 4 , \infty )$ D) $( - \infty , - 4 ) \cup ( - 3 , \infty )$ E) $( - \infty , - 3 ] \cup [ - 4 , \infty )$

Question

Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7 < - 1 \text { or } 2 x + 7 > 1$
A) $( - \infty , - 4 ] \cup [ - 3 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , - 3 ) \cup ( - 4 , \infty )$
D) $( - \infty , - 4 ) \cup ( - 3 , \infty )$
E) $( - \infty , - 3 ] \cup [ - 4 , \infty )$

Quizplus · Accepted Answer

First, solve each inequality separately: $2x+7<-1$ Subtracting 7 from both sides gives: $2x<-8$ Dividing both sides by 2 gives: $x<-4$ $2x+7>1$ Subtracting 7 from both sides gives: $2x>-6$ Dividing both sides by 2 gives: $x>-3$ The solution set is the union of these two sets: $(-\infty,-4)\cup(-3,\infty)$, which is answer choice D.

Solve the Compound Inequality 2x+7<−1 or 2x+7>12 x + 7 < - 1 \text { or } 2 x + 7 > 12x+7<−1 or 2x+7>1

Solve the Compound Inequality $2 x + 7 < - 1 \text { or } 2 x + 7 > 1$