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tomcenjerrym
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Does anyone can solve the following equation?
|x − 1| = 1 − x
Thanks
Tom
|x − 1| = 1 − x
Thanks
Tom
Square both sides. And see what you get.tomcenjerrym said:Does anyone can solve the following equation?
|x − 1| = 1 − x
Thanks
Tom
A more introductory way is to consider (x -1) as separately positive, and negative.Kummer said:Square both sides. And see what you get.
tomcenjerrym said:Does anyone can solve the following equation?
|x − 1| = 1 − x
Thanks
Tom
Sorry, that's unfair - it's your first post. Can you show us the work you have so far? Do you understand what absolute value means?
Actually, that is not an inequality question; but an absolute value equation.
Square both sides. And see what you get.
symbolipoint said:tomcenjerrym - Your first condition yields x=0 as a solution; and your second condition allows ALL real numbers as solutions. All real numbers will satisfy the equation.
You're correct. I was not careful enough when I solved the problem. We must watch around the critical point. The first part indicates x=1. When we check a value less than 1, we find equality; when we check a point greater than 1, we do not find equality.d_leet said:No they won't. Take x=5 as an example |5-1|=|4|=4, but 1-5=-4, so in this case |x-1| does not equal 1-x, hence it is obviously not true for all real numbers. There is, however, a subset of the real numbers (with more than a single element) that satisfies the above equation.
If you have |a| = -a, what is the only way this can be true?
To solve an inequality, you need to isolate the variable on one side of the inequality sign and keep the constant terms on the other side. Then, you can use inverse operations to solve for the variable. In this case, you can use addition and subtraction to isolate the variable.
The symbol "|" is called a bar or vertical line and it means "such that". It is used to separate the variable and the inequality expression.
Yes, an inequality can be solved with only one variable. In this case, the variable is "x".
In this case, the equal signs indicate that the expressions on both sides of the inequality are equal. This allows us to use inverse operations to solve for the variable.
The solution to this inequality is x = 1. This means that when x is equal to 1, the inequality is true. You can check this by plugging in x = 1 into the original inequality and seeing if it holds true.