Some applications of calculus use a mathematical structure called a power series. To find the interval of convergence of a power series, it is often necessary to solve an absolute value inequality. Solve the absolute value inequality below to find the interval of convergence
-$$\left| \frac { x + 1 } { 4 } \right|

Question

Some applications of calculus use a mathematical structure called a power series. To find the interval of convergence of a power series, it is often necessary to solve an absolute value inequality. Solve the absolute value inequality below to find the interval of convergence
-$$\left| \frac { x + 1 } { 4 } \right| < 1$$
A) $[ 0,3 ]$
B) $( - 5,3 )$
C) $[ - 5,3 ]$
D) $( 0,3 )$

Quizplus · Accepted Answer

To solve the inequality $\left| \frac { x + 1 } { 4 } \right| < 1$, we first remove the absolute value, giving us two inequalities: $\frac { x + 1 } { 4 } < 1$ and $\frac { x + 1 } { 4 } > -1$. Solving the first gives $x < 3$, and solving the second gives $x > -5$. Combining these gives the interval $(-5, 3)$.

Some Applications of Calculus Use a Mathematical Structure Called a Power