SOLUTION: Write the inequality and solve the problem: The difference of a number and 8 is less than 12.

Question 1191819: Write the inequality and solve the problem: The difference of a number and 8 is less than 12.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = unknown number
x-8 = difference of the number and 8
x-8 < 12 ... the result of translating the sentence into an inequality
i.e. the difference x-8 is smaller than 12

To solve this inequality, we add 8 to both sides.
This undoes the "minus 8" on the left side so x can be isolated.

x-8 < 12
x-8+8 < 12+8
x+0 < 20
x < 20

The unknown number is smaller than 20

For example, we could pick the value x = 15
x-8 < 12
15-8 < 12
7 < 12
we end up with a true statement, so the original statement is true when x = 15

On the other hand, if x is something larger than 20 (or 20 itself), then we get a false result.
Let's try something like x = 30
x-8 < 12
30-8 < 12
22 < 12
which is false

To graph x < 20 on the number line, you'll have an open circle at 20 and shading to the left.
The open circle will exclude the endpoint.

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