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How do you solve and write the following in interval notation: #2x - (7 + x) <= x#?

Answer 1

Savannah Anderson

#x in (-oo, oo)#

#2x - (7+x) <= x#

#=> 2x - 7 - x <= x#

#=> x - 7 <= x#

#=> -7 <= 0#

As the above is a tautology (always true, regardless of the value of #x#), the solution set is all real numbers. In interval notation, we can write this as having the endpoints of #+-oo#:

#x in (-oo, oo)#

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Answer 2

Jace Anderson

To solve and write the inequality (2x - (7 + x) \leq x) in interval notation, follow these steps:

Simplify the expression: (2x - (7 + x) \leq x)
(2x - 7 - x \leq x)
(x - 7 \leq x)
Move all terms involving (x) to one side of the inequality: (x - x \leq 7)
(0 \leq 7)
Since (0) is always less than or equal to (7), the solution is all real numbers.
Represent the solution in interval notation: ([-∞, +∞])

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and write the following in interval notation: #2x - (7 + x) &lt;= x#?

How do you solve and write the following in interval notation: #2x - (7 + x) <= x#?