I have a question. What's the answer to 9|x-2|-10>=-64? I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative. Thanks in advance.
I have a question. What's the answer to 9|x-2|-10>=-64? I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative. Thanks in advance.
I agree with your solution; your teacher might have been thinking about a different situation.
The inequality symbol ≥ means greater than OR equal.
As long as the left-hand side evaluates to a number that is greater than -64, the inequality is true. This happens for any value of x.
If you solved the inequality by hand, you ought to have reached this:
|x - 2| ≥ -6
This shows that x can be any Real number because |x-2| is non-negative, and any non-negative number is greater than -6.
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
Graphing each side of the given inequality is another way to solve it.
The graph of the left-hand side (green) lies entirely above the graph of the right-hand side (red).
In other words, at each value of x, the value of y on the green graph is greater than the value of y on the red graph.
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
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