Dividing both sides of the equation by 3 gives x = 12/3, which simplifies to 4. This basic linear equation is solved by isolating the variable.

According to the order of operations, multiplication is performed before addition. So, 3 * 2 = 6 and then 5 + 6 equals 11.

The area of a square is calculated by squaring the side length. In this case, 4^2 equals 16.

Dividing 8 by 4 yields 2. This illustrates a basic concept of division where the dividend is evenly divided by the divisor.

A prime number has exactly two distinct positive divisors: 1 and itself. Among the options provided, 7 fits this definition.

Adding 5 to both sides gives 2x = 14, and dividing both sides by 2 yields x = 7. This is a straightforward linear equation.

Multiply the coefficients 3 and 2 to get 6, and add the exponents on x (2 + 3 = 5) to achieve 6x❵. This uses the laws of exponents.

Subtract 2 from both sides to obtain 3y = 18, then divide by 3 to find y = 6. This simple linear manipulation isolates y.

The expression factors into (x - 3)(x + 3) = 0, giving the solutions x = 3 and x = -3. Recognizing a difference of squares is key here.

Parallel lines have identical slopes. Since the line y = 2x + 5 has a slope of 2, any parallel line must also have a slope of 2.

Subtract 3 from both sides to get 2x > 4, then divide by 2 to find x > 2. This inequality is solved by performing the same operation on both sides.

Substitute r = 3 into the formula C = 2πr to get C = 2π(3) = 6π. This uses the basic geometry formula for circumference.

The determinant of a 2x2 matrix [[a, b], [c, d]] is computed as ad - bc. Here, (1×4) - (2×3) = 4 - 6, which equals -2.

x² - 9 is a difference of squares and can be expressed as (x - 3)(x + 3). Recognizing this pattern is essential for factorization.

Simplifying (4x)/2 yields 2x = 8, and dividing both sides by 2 gives x = 4. This is a straightforward division problem.

Factoring the quadratic gives (x - 2)(x - 3) = 0, which leads to x = 2 and x = 3 as the solutions. This demonstrates using factorization for solving quadratics.

Recognize that 81 is 3^4. Setting 3^(2x) equal to 3^4 means that 2x = 4. Dividing by 2, we find that x = 2.

Let the width be w and the length be 2w. The area is then 2w² = 50, so w² = 25, giving w = 5. Only the positive value is acceptable for a width.

The sequence has a common difference of 4. With the first term 3 and the last term 39, there are 10 terms. Using the formula for the sum of an arithmetic sequence gives 10*(3+39)/2 = 210.

Applying the Pythagorean theorem, the hypotenuse is calculated as √(3² + 4²) = √(9 + 16) = √25, which equals 5. This familiar 3-4-5 triangle is a classic example in geometry.