Question

The symbol $\left|a\right|$ means $+a$ if $a$ is greater than or equal to zero and $-a$ if $a$ is less than or equal to zero; the symbol M means "less than"; the symbol > means "greater than"
The set of values $x$ satisfying the inquality $|3-x|<4$ consists of all $x$ such that:

• A. $x^2<49$
• B. $x^2>1$
• C. $1>x^2<49$
• D. $-1<x<7$
• E. $-7<x<1$

Answer 1

The correct option is D $-1<x<7$

Let $AB$ be a straight line segment with its midpoint at $3$, and its right end at $B$. Each if the two intervals from $A$ to $3$ and from $3$ to $B$ is less than $4$. Hence $B$ is to the left of $7$ and $A$ is to the right of $-1$ or
if $x\le 3,|x-3|<4$ means $3-x<4.\therefore -1<x;$
if $x>3,|x-3|<4$ means $x-3<4\Rightarrow x<7$

$\Rightarrow -1<x<7$