Solve the compound inequality using the compact form. Express the solution sets in interval notation. $- 2

Question

Solve the compound inequality using the compact form. Express the solution sets in interval notation. $- 2 < 1 - x < 2$
A) $( - 3,1 )$
B) $( - 1,3 )$
C) $( - \infty , - 1 )$
D) $( - \infty , 3 )$
E) $( - 1 , \infty )$

Quizplus · Accepted Answer

To solve the compound inequality using compact form, we need to isolate the variable in the middle and express the inequality in a form of "lower bound < variable < upper bound". Starting with the given inequality: $$-2<1-x<2$$ We can subtract 1 from all three parts: $$-2-1<1-x-1<2-1$$ $$-3<-x<1$$ Then, we multiply all three parts by -1, but we need to reverse the inequality signs because we're multiplying by a negative number: $$3>x>-1$$ This is the desired form, so the solution set is $(-1,3)$ in interval notation. Thus, the answer is B.

Solve the Compound Inequality Using the Compact Form −2<1−x<2- 2 < 1 - x < 2−2<1−x<2

Solve the Compound Inequality Using the Compact Form $- 2 < 1 - x < 2$