Question

The rules for a book reprt say that the report should have 300 words with an absolute deviation of at most 20 words. Write and solve an absolute value inequality that represents the acceptable number of words.

Answer 1

Equation; |x-300| is equal to or less than 20

Solved; 280 is equal to or less than x is less than or equal to 320

Explanation:

Since the equation is |x-300| is equal to or less than 20 you solve like this:

|x-300| is equal to or less than 20

add 300 to both sides

x is equal to or less than 320

Then since it's an absolute value equation you must do:

|x-300| is equal to or less than -20

add 300 to both sides

x is equal to or greater than 280

Altogether that should be:

280 is equal to or less than x is less than or equal to 320

Answer 2

Inequality:
`|x-300|\geq 20`

Inquality solved:
`280\leq x\leq 320`

Explanation:

You need to remember the meaning of the inequalities symbols:

`<` : Less than.

`>` : Greater than.

`\leq` : Less than or equal to.

`\geq` : Greater than or equal to.

Let be "x" the acceptable number of words.

Knowing that the resport should have 300 words with an absolute deviation of at most 20 words, you can write the following bsolute value inequality:

`|x-300|\geq 20`

In order to solve it, you need to sep up two cases.

Case 1. The expression
`x-300` is positive:

`x-300\geq 20`

Solve for "x":

`x-300\geq 20\\\\x\geq 20+300\\\\x\geq320`

Case 2. The expression
`x-300` is negative:

`x-300\leq - 20`

Solve for "x":

`x-300\leq -20\\\\x\leq -20+300\\\\x\leq 280`

Therefore, you get:

`280\leq x\leq 320`