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# System prepended metadata

title: Sample midterm exam F

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**Problem 1.** Perform the addition of the following algebraic fractions.
$$
\frac{1}{9x + 2y} - \frac{2}{9x - 2y}
$$

**Problem 2.** Solve the following equation in the set of real numbers.
$$
7-\frac{7x + 56}{5} = 3x + 9
$$

**Problem 3.** Determine the solution set of the following system of equations.
$$
7x + 7y = -21 \ \ \ \ \ \ \ \ \ 
9y + 42 = -4x
$$

**Problem 4.** Solve the following inequality in the set of real numbers and give the solution set in interval notation.
$$
|5x + 2| + 9 \geq 0
$$

**Problem 5.** Simplify the following expression by rationalizing the denominator.
$$
\frac{64}{\sqrt{3} + \sqrt{11}}
$$

**Problem 6.** Solve the following equation in the set of real numbers.
$$
\sqrt{1 - x} \cdot \sqrt{3 - x} = 2
$$

**Problem 7.** Graph the function given by the following formula and determine its largest possible domain and range in interval notation.
$$
f(x) = - (x + 4)(x + 6)
$$

**Problem 8.** The price of a product is first increased by 11%, then decreased 4 times, each time by 4%. By how much has the product’s price changed overall?

**Problem 9.** The equation of a line is $5x + 6y = -1.$ Determine the equation of the line perpendicular to it that passes through the point $(6, -7).$

**Problem 10.** In a right triangle, the hypotenuse is 14 cm long and one leg is 13 cm long. Find the measure of the angle at the vertex opposite the given leg.