Algebra Class Quiz

Solving Equations

• To solve for x in the equation 2x + 3 = 11, you would use subtraction and division.
• First, subtract 3 from both sides to isolate the 2x term.
• Then, divide both sides by 2 to solve for x.

Greatest Common Divisor

• The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
• The GCD of 36 and 60 is 12.

Coefficients

• In a polynomial expression, the coefficient is the numerical factor that multiplies a variable.
• In the equation y = 3x² + 2x - 5, the coefficient of x is 2.

Function Composition

• Function composition involves combining two or more functions.
• The notation (f ∘ g)(x) represents the composition of function f with function g.
• To calculate (f ∘ g)(2), first find g(2), which is 2² = 4.
• Then, substitute 4 into the function f(x) to find f(4), which is 2(4) + 4 = 12.
• Therefore, (f ∘ g)(2) is 12.

Properties of Equality

• Properties of equality are rules that allow you to manipulate equations while preserving their truth.
• Some common properties include the reflexive property (a = a), the symmetric property (if a = b, then b = a), and the transitive property (if a = b and b = c, then a = c).
• One property that is NOT a property of equality is the distributive property.
• The distributive property states that a(b + c) = ab + ac, which is a property of multiplication, not equality.