SOLUTION: Solve the following inequality for x. express your answer in interval notation.show algebriac steps: 2x- (7+x)<_x my work= 2x- 7-x<x x-7<x x-x-7<x-x

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Question 202507: Solve the following inequality for x. express your answer in interval notation.show algebriac steps: 2x- (7+x)<_x

my work= 2x- 7-x x-7 x-x-7 -7<0
interval notation: (7,0)

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Your work is perfectly correct up to your conclusion!

You got

but you interpreted it incorrectly.

When is -7 less than 0? Answer: Always!

The key here is to notice that there is no "x" in your final inequality. The x's all ended up being canceled out. This means the value of "x" has no effect on the truth (or lack thereof) of the inequality. Since -7 is always less than 0, your solution is "All real numbers". In other words, any number will work for "x" in the original inequality!

In interval notation this is: (-infinity, infinity). (Replace the word "infinity" with the infinity symbol.)

If you had gotten an inequality without an x which was never true, then that would mean NO values for x could ever make the inequality true. In other words: "No solution". For example there would be no solution if you ended up with something like: 10 > 20

If you are solving an equation and the variable(s) disappear like x did above, then the interpretation is still the same. Either all numbers or no numbers will be solutions based on whether the resulting x-less equation is always true or always false.

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