Solve the inequality. 7|x+2|+5&gt;4

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Solve the inequality.   7|x+2|+5&amp;gt;4

Rita Miller · Accepted Answer

Step 1&amp;nbsp;By using constants, we can add, subtract, multiply, and divide to solve the absolute value inequality. The crucial point is that the absolute inequality is reversed if we multiply or divide using any negative number.The absolute inequality can be solved by using the formula ,&amp;nbsp;If&amp;nbsp;|x−a|≤r, then&amp;nbsp;−r≤x−a≤r,&amp;nbsp;|x−a|≥r, then&amp;nbsp;|x−a|≤−r&amp;nbsp;Also we use the form that |x|=|-x|=x .&amp;nbsp;Step 2&amp;nbsp;Consider the absolute inequality 7|x+2|+5&amp;gt;4,&amp;nbsp;We can start solving the inequality by subtracting 5 on both side,&amp;nbsp;7|x+2|+5-5&amp;gt;4-5&amp;nbsp;7|x+2|&amp;gt;-1&amp;nbsp;Now divide by 7 on both sides, we get&amp;nbsp;7|x+2|7&amp;gt;−17&amp;nbsp;|x+2|&amp;gt;−17&amp;nbsp;Thus in the last inequality , For any x both positive and negative we only get positive value from the absolute equation,&amp;nbsp;We know that |x|=|-x|=x,&amp;nbsp;There for any real number&amp;nbsp;|x+2|&amp;gt;−17&amp;nbsp;is true.&amp;nbsp;Thus x can be any real number&amp;nbsp;x∈R, where R denoting real numbers .&amp;nbsp;Hence the interval form of the solution is&amp;nbsp;x∈(−∞,∞).

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

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