Algebraic Concepts & Quantitative Reasoning Flashcards

What is the value of x in the equation 2x + 4 = 12?

Answer: 6

To solve the equation 2x + 4 = 12, first isolate the term with x by subtracting 4 from both sides, which gives 2x = 8. Next, divide both sides by 2 to solve for x. This results in x = 4. (Note: The provided correct answer '6' is incorrect for the given equation; x=4 is the correct solution.)

What is the slope of the line represented by y = 3x + 2?

Answer: 3

A linear equation in the form y = mx + b is known as the slope-intercept form. In this standard form, 'm' directly represents the slope of the line. For the equation y = 3x + 2, the coefficient of x is 3, which is the slope.

Simplify: 5(x + 2) − 3x

Answer: 2x + 10

To simplify the expression 5(x + 2) − 3x, first apply the distributive property to 5(x + 2), which yields 5x + 10. Then, combine the like terms (5x and -3x). This simplifies to 2x + 10.

If f(x) = x² − 4x, what is f(3)?

Answer: -1

To evaluate f(3) for the function f(x) = x² − 4x, substitute 3 for every 'x' in the expression. This calculation becomes (3)² − 4(3), which simplifies to 9 − 12. Therefore, f(3) = -3. (Note: The provided correct answer '-1' is incorrect for the given function; -3 is the correct evaluation.)

Which expression is equivalent to (x + 3)(x - 3)?

Answer: x² - 9

The expression (x + 3)(x - 3) is a special product known as the difference of squares. When multiplying two binomials of the form (a + b)(a - b), the result is a² - b². In this case, a = x and b = 3, so the product is x² - 3², which simplifies to x² - 9.

What is the solution to the inequality 3x − 5 < 10?

Answer: x < 5

To solve the inequality 3x − 5 < 10, first add 5 to both sides to isolate the term with x, resulting in 3x < 15. Then, divide both sides by 3. This yields x < 5.

Which value of x satisfies the equation x² = 49?

Answer: ±7

To solve the equation x² = 49, you need to find the numbers that, when squared, equal 49. Taking the square root of both sides gives x = ±√49. Therefore, x can be both positive 7 and negative 7, as both (7)² and (-7)² equal 49.

Evaluate: |−12 + 7|

Answer: 5

First, perform the operation inside the absolute value bars: -12 + 7 equals -5. The absolute value of a number represents its distance from zero on the number line, always resulting in a non-negative value. Therefore, |−5| is 5.

Which graph represents a linear function?

Answer: A straight line

A linear function is characterized by a constant rate of change, which means its graph will always be a straight line. Options like U-shaped, zigzag, or circular curves represent other types of functions or relations, not linear ones.