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How do you write an inequality and solve given "a number decreased by 8 is less than 21"?

Answer 1

Eva Abramson

See the entire solution process below:

First, write the inequality.

Let's call the number we will be solving for #n#.

Therefore "a number decreased by 8" can be written as:

#n - 8#

"is less than 21" can be written as:

#< 21#

Putting this altogether gives:

#n - 8 < 21#

To solve for #n# add #color(red)(8)# to each side of the inequality which will solve for #n# while keeping the inequality balanced:

#n - 8 + color(red)(8) < 21 + color(red)(8)#

#n - 0 < 29#

#n < 29#

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Answer 2

Kennedy Adams

To write the inequality and solve the given statement "a number decreased by 8 is less than 21," you would represent the situation as follows:

Let x be the number.

The inequality would be: x - 8 < 21.

To solve for x:

Add 8 to both sides of the inequality: x - 8 + 8 < 21 + 8 x < 29

So, the solution to the inequality is x < 29.

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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.