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 , then ,
Also we use the form that |x|=|-x|=x .
Consider the absolute inequality 7|x+2|+5>4,
We can start solving the inequality by subtracting 5 on both side,
Now divide by 7 on both sides, we get
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 is true.
Thus x can be any real number , where R denoting real numbers .
Hence the interval form of the solution is .
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