Sharon worked hard for a long time to save the money for a new car. She has budgeted between $15,000 and $20,000 for the new car plus the cost of gas for a year. Let x represent gas mileage. Which compound inequality represents the gas mileage that a $12,000 car can get and still fit in her budget if gas costs $4 per gallon and she drives 15,000 miles a year? 15,000 ≤ 12,000 + 415,000 less than or equal to 12,000 plus 4 left-parenthesis StartFraction 15,000 over x EndFraction right-parenthesis less than or equal to 20,000. ≤ 20,000 15,000 < 12,000 + 415,000 less than 12,000 plus 4 left-parenthesis StartFraction 15,000 over x EndFraction right-parenthesis less than 20,000. < 20,000 15,000 ≤ 12,000 + x15,000 less than or equal to 12,000 plus x left-parenthesis StartFraction 15,000 over 4 EndFraction right-parenthesis less than or equal to 20,000. ≤ 20,000 15,000 < 12,000 + x15,000 less than 12,000 plus x left-parenthesis StartFraction 15,000 over 4 EndFraction right-parenthesis less than 20,000. < 20,000

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Answer:

I can confirm it's A

[tex]15000 \leqslant 12000 + 4( \frac{15000}{x} ) \leqslant 20000[/tex]

Step-by-step explanation:

E2020

The gas mileage illustrates compound and linear inequalities.

The compound inequality is (a) [tex]\mathbf{15000 \le 12000 + 4 \times \frac{15000}{x} \le 20000}[/tex]

The budget is given as: an amount between $15,000 and $20,000

The initial amount is given as:

[tex]\mathbf{Initial = \$12000}[/tex]

[tex]\mathbf{Rate = \$4\ per\ gallon}\\[/tex]

[tex]\mathbf{Max = 15000\ miles}[/tex]

Let x represent the gas mileage.

So, the cost function is:

[tex]\mathbf{C(x) = Initial + Rate \times \frac{Max}{x}}[/tex]

This gives

[tex]\mathbf{C(x) = 12000 + 4 \times \frac{15000}{x}}[/tex]

The cost is between $15000 and $20000.

So, we have:

[tex]\mathbf{15000 \le 12000 + 4 \times \frac{15000}{x} \le 20000}[/tex]

Hence, the compound inequality is (a) [tex]\mathbf{15000 \le 12000 + 4 \times \frac{15000}{x} \le 20000}[/tex]

Read more about compound linear inequalities at:

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