Answer:
Inequality: [tex]|x-300|\geq 20[/tex]
Inquality solved: [tex]280\leq x\leq 320[/tex]
Step-by-step explanation:
You need to remember the meaning of the inequalities symbols:
[tex]<[/tex] : Less than.
[tex]>[/tex] : Greater than.
[tex]\leq[/tex] : Less than or equal to.
[tex]\geq[/tex] : 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:
[tex]|x-300|\geq 20[/tex]
In order to solve it, you need to sep up two cases.
Case 1. The expression [tex]x-300[/tex] is positive:
[tex]x-300\geq 20[/tex]
Solve for "x":
[tex]x-300\geq 20\\\\x\geq 20+300\\\\x\geq320[/tex]
Case 2. The expression [tex]x-300[/tex] is negative:
[tex]x-300\leq - 20[/tex]
Solve for "x":
[tex]x-300\leq -20\\\\x\leq -20+300\\\\x\leq 280[/tex]
Therefore, you get:
[tex]280\leq x\leq 320[/tex]
