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# Linear Inequalities

## Solve one-step inequalities

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Hybrid Cars

Credit: Parker Knight
Source: http://www.flickr.com/photos/rocketboom/6464284933/

Did you know that most hybrid cars are fuel-efficient only when you’re making frequent stops? If you’re driving on a highway at a more or less constant speed, the fuel efficiency of hybrids is usually not higher than the efficiency of standard, gasoline-driven cars. In addition, hybrid cars cost more than non-hybrid cars to purchase. At what point does it become cost-efficient to buy a hybrid car?

#### Fuel Efficiency

Any vehicle that combines two or more sources of power to provide propulsion is considered a hybrid. Most hybrid cars on the road right now are gasoline-electric hybrids; they can operate using gas in their tanks or electricity from their batteries—or at times, both (when you need a little extra boost driving uphill, for instance). When you’re driving in the city, you have to make frequent stops at traffic lights. Every time you hit the brakes, you lose the momentum you had and that energy is completely wasted. On top of that, your engine keeps running while you’re waiting at a red light and that burns gas! What a hybrid car does is transform these wasted energies into electric energy that is stored in its battery. While driving, a hybrid car can also stop its use of the gasoline engine and operate only using the battery during coasting and slow-down phases.

Credit: Laura Guerin
Source: CK-12 Foundation

If a gasoline car gets \begin{align*}x_{gas}\end{align*} miles per gallon and a hybrid gets \begin{align*}x_{hybrid}\end{align*} miles per gallon, then the relation \begin{align*}x_{hybrid} \ge x_{gas}\end{align*} is always true! There’s no way you’ll be using more gas with hybrid cars; sometimes it will be substantially less than the amount used by standard cars, and at other times the two quantities can be equal.

#### Explore More

Hybrid cars definitely contribute less pollution to the environment, and they help reduce our dependency on fossil fuels. However, for most people, the choice between a hybrid and a standard car all comes down to the overall cost-efficiency.

Let’s say you drive 15,000 miles a year and the cost of gas is $3.50 a gallon. You’re trying to decide whether to buy a standard or a hybrid car. The hybrid gives you 30 miles per gallon (mpg) and the standard gives you 20 mpg. The hybrid car costs you$5,000 more than the standard. How long would it take for your savings on fuel to surpass the additional cost of the hybrid vehicle?

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