Solve the inequality. 7|x+2|+5>4

Step 1
We can solve the absolute value inequality by adding , subtracting , multiplying and dividing with constants . The important thing is that if we multiply or divide by using any negative number, then the absolute inequality reverses .
The absolute inequality can be solved by using the formula ,
If ${\displaystyle |x-a|\le r}$, then ${\displaystyle -r\le x-a\le r}$,
${\displaystyle |x-a|\ge r}$, then ${\displaystyle |x-a|\le -r}$
Also we use the form that |x|=|-x|=x .
Step 2
Consider the absolute inequality 7|x+2|+5>4,
We can start solving the inequality by subtracting 5 on both side,
7|x+2|+5-5>4-5
7|x+2|>-1
Now divide by 7 on both sides, we get
${\displaystyle \frac{7|x+2|}{7}>\frac{-1}{7}}$
${\displaystyle |x+2|>\frac{-1}{7}}$
Thus in the last inequality , For any x both positive and negative we only get positive value from the absolute equation,
We know that |x|=|-x|=x,
There for any real number ${\displaystyle |x+2|>\frac{-1}{7}}$ is true.
Thus x can be any real number ${\displaystyle x\in R}$, where R denoting real numbers .
Hence the interval form of the solution is ${\displaystyle x\in (-\mathrm{\infty },\mathrm{\infty })}$.