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Answer:
[tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]
Both are different forms to represent the same: the amount of gas is between 9.8 gallons and 10.2 gallons, including the borders.
Explanation:
1. Relation between the number of gallons of gas pumped and the total amount paid:
[tex]Number\text{ }of\text{ }gallons=amount\text{ }paid(\$)/price(\$/gallon)[/tex]
2. Conversion
The amount paid is said to be $ 25 ± $0.50
To transform that into number of gallons, divide by the price of the regular gas: $2.50/gallon
[tex]Number\text{ }of\text{ }gallons=\$25/(\$2.50/gallon)\pm$0.50/(\$2.50/gallon)[/tex]
[tex]Number\text{ }of\text{ }gallons=10gallons\pm0.2gallon[/tex]
3. Absolute value equation (inequality)
- 10 gallons ± 0.2 gallons converted to an absolute value inequality is:
[tex]|x-10gallons|=0.2gallons[/tex]
Solution:
[tex]-0.2\leq x-10\leq 0.2[/tex]
[tex]-0.2+10\leq x\leq 0.2+10[/tex]
[tex]9.8\leq x\leq 10.2[/tex]
Hence, the solution is:
[tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]
