Solve the inequality. $\left| \frac { x - 2 } { 5 } \right|

Question

Solve the inequality. $\left| \frac { x - 2 } { 5 } \right| < 6$
A) $( - 28,2 ) \cup ( 2,32 )$
B) $( - 28,32 )$
C) $( - \infty , 28 ) \cup ( 32 , \infty )$
D) $\phi$

Quizplus · Accepted Answer

First, we isolate the absolute value expression by multiplying both sides by 5: $|x-2|<30$. This inequality is equivalent to the following two inequalities: $$x-2<30 \qquad \text{and} \qquad x-2>-30$$ Simplifying each inequality, we get $x<32$ and $x>-28$. The interval notation for this solution is $(-28,32)$, so the answer is B.

Solve the Inequality ∣x−25∣<6\left| \frac { x - 2 } { 5 } \right| < 6​5x−2​​<6

Solve the Inequality $\left| \frac { x - 2 } { 5 } \right| < 6$