What is an algebraic expression?

An algebraic expression is a mathematical phrase that can include numbers, variables (letters representing unknown values), and arithmetic operations (such as addition, subtraction, multiplication, and division). For example, 3x + 5 is an algebraic expression.

What is the difference between an equation and an expression?

An expression is a combination of numbers, variables, and operations without an equality sign, whereas an equation is a statement that two expressions are equal, indicated by an equality sign. For example, 2x + 3 is an expression, while 2x + 3 = 7 is an equation.

How do you solve the equation 2x + 3 = 11?

Hint: Isolate the variable x.

To solve for x, first, subtract 3 from both sides: 2x = 11 - 3, which simplifies to 2x = 8. Then, divide both sides by 2: x = 8 / 2, resulting in x = 4.

What is the distributive property in algebra?

The distributive property states that a(b + c) = ab + ac. This means you can distribute the multiplication of a term across a sum or difference inside parentheses. For example, 2(3 + 4) = 2*3 + 2*4 = 6 + 8 = 14.

If x = 3, evaluate the expression 4x² - 2x + 1.

To evaluate the expression for x = 3, substitute 3 for x: 4(3²) - 2(3) + 1 = 4(9) - 6 + 1 = 36 - 6 + 1 = 31.

What is a linear equation?

A linear equation is an equation that makes a straight line when graphed. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

What is the formula for the area of a rectangle?

The area A of a rectangle is given by the formula A = length × width. For example, if the length is 5 and the width is 3, then A = 5 × 3 = 15.

How do you simplify the expression 3(x + 4) - 2(x - 1)?

Hint: Use the distributive property.

First, apply the distributive property: 3x + 12 - 2x + 2. Combine like terms: (3x - 2x) + (12 + 2) = x + 14.

What is the quadratic formula?

The quadratic formula is used to find the solutions of a quadratic equation ax² + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

If f(x) = 2x + 3, what is f(5)?

To find f(5), substitute 5 for x: f(5) = 2(5) + 3 = 10 + 3 = 13.

What is the difference between a monomial and a polynomial?

A monomial is an algebraic expression with only one term (e.g., 5x²), while a polynomial is an expression composed of multiple terms (e.g., 3x² + 2x + 1).

What does it mean for two expressions to be equivalent?

Two expressions are equivalent if they have the same value for all values of the variables involved. For example, 2(x + 1) and 2x + 2 are equivalent.

How do you factor the expression x² + 5x + 6?

Hint: Look for two numbers that multiply to 6 and add to 5.

The expression factors to (x + 2)(x + 3) because 2 and 3 multiply to 6 and add to 5.

What is an exponential equation?

An exponential equation is an equation in which variables appear in the exponent. For example, 2^x = 8 is an exponential equation.

If 3x + 4 = 19, what is the value of x?

Hint: Isolate x by performing inverse operations.

First, subtract 4 from both sides: 3x = 19 - 4, which simplifies to 3x = 15. Then, divide both sides by 3: x = 15 / 3, resulting in x = 5.