simplify the expression 2x 3x 5
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ATI TEAS 7

TEAS Test Math Questions

1. Simplify the expression: 2x + 3x - 5.

Correct answer: A

Rationale: To simplify the expression 2๐‘ฅ + 3๐‘ฅ - 5, follow these steps: Identify and combine like terms. The terms 2๐‘ฅ and 3๐‘ฅ are both 'like terms' because they both contain the variable ๐‘ฅ. Add the coefficients of the like terms: 2๐‘ฅ + 3๐‘ฅ = 5๐‘ฅ. Simplify the expression. After combining the like terms, the expression becomes 5๐‘ฅ - 5, which includes the simplified term 5๐‘ฅ and the constant -5. Thus, the fully simplified expression is 5๐‘ฅ - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

2. The phone bill is calculated each month using the equation y = 50x. The cost of the phone bill per month is represented by y and x represents the gigabytes of data used that month. What is the value and interpretation of the slope of this equation?

Correct answer: D

Rationale: The slope of the equation y = 50x is 50, which means that for each additional gigabyte of data used, the cost increases by 50 dollars. Therefore, the interpretation of the slope is that it represents the cost per gigabyte, making '50 dollars per gigabyte' the correct answer. Choices A, B, and C are incorrect because they do not reflect the relationship between the cost and the amount of data used in the given equation.

3. If a train travels 60 miles per hour for 2 hours, how far does the train travel?

Correct answer: C

Rationale: To find the distance traveled by the train, we use the formula Distance = Speed x Time. Given that the train travels at 60 miles per hour for 2 hours, the calculation would be 60 miles/hour x 2 hours = 120 miles. Therefore, the correct answer is 120 miles. Choice A (60 miles) is incorrect because it only represents the speed of the train, not the total distance traveled. Choice B (100 miles) is incorrect as it does not account for the full 2 hours of travel. Choice D (200 miles) is incorrect as it overestimates the distance by multiplying the speed by the time incorrectly.

4. A driver drove 305 miles at 65 mph, stopped for 15 minutes, then drove another 162 miles at 80 mph. How long was the trip?

Correct answer: B

Rationale: To find the total trip duration, calculate the driving time for each segment and add the stop time. The driving time for the first segment is 305 miles รท 65 mph = 4.69 hours. The driving time for the second segment is 162 miles รท 80 mph = 2.025 hours. Adding the 15-minute stop (0.25 hours) gives a total time of 4.69 hours + 2.025 hours + 0.25 hours = 6.965 hours, which is closest to 6.69 hours (Choice B). Option A is incorrect as it miscalculates the total duration. Option C is incorrect as it overestimates the total duration. Option D is incorrect as it underestimates the total duration.

5. What is the least common denominator of two fractions?

Correct answer: C

Rationale: The least common denominator of two fractions is the least common multiple of both denominators. This is because the least common denominator is the smallest number that both denominators can divide into evenly, ensuring that both fractions can be expressed with a common denominator. Choice A is incorrect as the least common denominator is a multiple of both denominators, not a number that multiplies into both. Choice B is incorrect because the common denominator needs to be a multiple of both denominators, not just a number they can divide into evenly. Choice D is incorrect as the greatest common factor is not used to find the least common denominator, but rather the least common multiple.

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