 # Solve the inequality. 7|x+2|+5>4 Michael Maggard 2021-12-09 Answered
Solve the inequality.
7|x+2|+5>4
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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 $|x-a|\le r$, then $-r\le x-a\le r$,
$|x-a|\ge r$, then $|x-a|\le -r$
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
$\frac{7|x+2|}{7}>\frac{-1}{7}$
$|x+2|>\frac{-1}{7}$
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 $|x+2|>\frac{-1}{7}$ is true.
Thus x can be any real number $x\in R$, where R denoting real numbers .
Hence the interval form of the solution is $x\in \left(-\mathrm{\infty },\mathrm{\infty }\right)$.