Algebraic Expressions & Equations Flashcards

What is the correct simplified form of 2x + 3x?

Answer: 5x

This question tests the basic algebraic principle of combining like terms. When terms have the same variable raised to the same power, their coefficients can be added together. Here, 2x and 3x are like terms, so adding their coefficients (2 + 3) results in 5, keeping the variable x to give 5x.

Solve for x in the equation 5x - 3 = 12.

Answer: x = 3

To solve for x, we need to isolate it on one side of the equation. First, add 3 to both sides: 5x - 3 + 3 = 12 + 3, which simplifies to 5x = 15. Next, divide both sides by 5: 5x / 5 = 15 / 5, which yields x = 3.

Which of the following is the correct expanded form of (x + 2)(x + 3)?

Answer: x² + 5x + 6

To expand the expression (x + 2)(x + 3), we use the FOIL method (First, Outer, Inner, Last). This involves multiplying the First terms (x * x = x²), Outer terms (x * 3 = 3x), Inner terms (2 * x = 2x), and Last terms (2 * 3 = 6). Combining these results in x² + 3x + 2x + 6, which simplifies to x² + 5x + 6.

What is the solution to the equation 2x + 3 = 7?

Answer: x = 2

To solve for x, we first need to isolate the term with x. Subtract 3 from both sides of the equation: 2x + 3 - 3 = 7 - 3, which simplifies to 2x = 4. Then, divide both sides by 2: 2x / 2 = 4 / 2, resulting in x = 2.

Which of the following represents the equation for the area of a rectangle?

Answer: Area = length × width

The area of a rectangle is a fundamental geometric concept representing the amount of surface it covers. This is universally calculated by multiplying its length by its width. The formula Area = length × width is the correct and standard equation for this calculation.

Simplify the expression 4x - 2x + 7.

Answer: 2x + 7

To simplify the expression 4x - 2x + 7, we combine the like terms. The terms 4x and -2x both contain the variable x, so their coefficients can be subtracted: 4 - 2 = 2. This leaves 2x. The constant term +7 has no other like terms, so the simplified expression is 2x + 7.

Which of the following is the factored form of x² + 5x + 6?

Answer: (x + 2)(x + 3)

To factor a quadratic expression of the form x² + bx + c, we look for two numbers that multiply to c (the constant term, 6) and add up to b (the coefficient of x, 5). The numbers 2 and 3 satisfy these conditions, as 2 * 3 = 6 and 2 + 3 = 5. Therefore, the factored form is (x + 2)(x + 3).

What is the solution to the equation x/3 = 4?

Answer: x = 12

To solve for x in the equation x/3 = 4, we need to isolate x. Since x is being divided by 3, the inverse operation is multiplication. Multiply both sides of the equation by 3: (x/3) * 3 = 4 * 3. This simplifies to x = 12.

Which of the following is the correct simplified form of (3x + 4)(2x + 1)?

Answer: 6x² + 11x + 4

To simplify the expression (3x + 4)(2x + 1), we use the FOIL method. Multiply the First terms (3x * 2x = 6x²), Outer terms (3x * 1 = 3x), Inner terms (4 * 2x = 8x), and Last terms (4 * 1 = 4). Combining these terms gives 6x² + 3x + 8x + 4, which simplifies to 6x² + 11x + 4.