Subtract 3 from both sides to obtain 2x = 4, then divide both sides by 2 to get x = 2. This step”by”step approach is standard for solving simple linear equations.

Using the distributive property, multiply 3 by each term inside the parentheses to obtain 3x + 12. This clearly demonstrates the basic distribution process.

The commutative property of multiplication states that changing the order of the factors does not change the product. Therefore, ab = ba is a direct application of this property.

Dividing both sides of the equation 5y = 20 by 5 isolates y, yielding y = 4. This is a straightforward application of inverse operations.

By combining like terms, x + 3x gives 4x and then subtracting 2 results in 4x - 2. This is a basic demonstration of combining similar terms.

Distribute 3 to obtain 6x - 12 = 18. Adding 12 to both sides gives 6x = 30, and dividing by 6 isolates x as 5.

Recognizing 4x² - 9 as a difference of squares, it factors into (2x)² - (3)², which can be rewritten as (2x - 3)(2x + 3).

Adding the two equations eliminates y, leading to 2x = 12 and thus x = 6. Substituting x back into one of the original equations provides y = 4.

The numbers 2 and 3 multiply to 6 and add to 5, which allows the quadratic to be factored as (x + 2)(x + 3). This technique is a basic factorization method.

Multiplying the numerator gives 6x❵ and dividing by 6x❴ leads to x^(5-4) which is x. The coefficients cancel perfectly and the exponents are subtracted.

Substituting x = 3 into f(x) = 2x + 1 yields f(3) = 2(3) + 1 = 7. This evaluation follows the basic function substitution rule.

Dividing the entire equation by 2 transforms it into y = 2x + 3, making it clear that the slope is the coefficient of x, which is 2.

Cross-multiplying gives 1 = 2(x - 1). Solving this equation leads to x - 1 = 1/2 and finally x = 3/2. This process adheres to standard techniques for solving rational equations.

Calculating the square roots gives √49 = 7 and √9 = 3. Their sum, 7 + 3, is 10, which is the simplified result.

First add 2 to both sides to isolate x/3, yielding x/3 = 3. Multiplying both sides by 3 gives x = 9, which is the correct solution.

Factoring the quadratic gives (x - 2)(x - 3) = 0. Setting each factor equal to zero yields the solutions x = 2 and x = 3.

The vertex of a parabola in the form f(x) = ax² + bx + c is found using the formula -b/(2a) for the x-coordinate. Substituting x = 2 into the function gives the y-coordinate -1, so the vertex is (2, -1).

Cross-multiplying yields x = 3(x - 2). Expanding and rearranging the equation gives 2x = 6, so x = 3. It is important to verify that the solution does not make the denominator zero.

The equation log₂(x) = 3 implies that 2 raised to the power of 3 equals x. Since 2³ is 8, the value of x is 8.

Substitute x = 3 into the equation to get 2(3) - k = 4, which simplifies to 6 - k = 4. Solving for k gives k = 2, ensuring the point lies on the line.