How do you solve |- 7x - 1| = 50|−7x−1|=50?

1 Answer
Mr. X.
Apr 16, 2018

x\in{-51/7; 7}x∈{−517;7}

Explanation:

We have:

|-7x-1|=50|−7x−1|=50

If the absolute value of an expression is equal to a certain quantity, then the expression's value must either equal the quantity itself or its opposite. Therefore, we can deduce that:

-7x-1\in{-50;50}−7x−1∈{−50;50}

-(7x+1)\in{-50;50}−(7x+1)∈{−50;50}

Multiplying both sides by -1−1:

7x+1\in{-50; 50}7x+1∈{−50;50}

Subtracting 11 and dividing by 77:

x\in{(-50-1)/7;(50-1)/7}x∈{−50−17;50−17}

x\in{-51/7; 7}x∈{−517;7}

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