Algebraic Expressions and Equations

Front

What is an algebraic expression?

Back

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. For example, 3x + 5 is an algebraic expression.

Front

What is the difference between an equation and an expression?

Back

An equation is a statement that two expressions are equal, often containing an equals sign (e.g., 2x + 3 = 7). An expression does not have an equals sign.

Front

How do you solve the equation 3x + 2(4x - 4) = 3?

Back

First, distribute: 3x + 8x - 8 = 3. Combine like terms: 11x - 8 = 3. Add 8 to both sides: 11x = 11. Divide by 11: x = 1.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and reduce it to its simplest form.

Front

What is a coefficient in an algebraic expression?

Back

A coefficient is a numerical factor that multiplies a variable in an expression. For example, in 4x, 4 is the coefficient.

Front

What is a variable in algebra?

Back

A variable is a symbol, often a letter, that represents an unknown value in an expression or equation. For example, x and y are variables.

Front

How do you combine like terms in the expression 5x - 6x - 8x + 7?

Back

Combine the coefficients of like terms: (5 - 6 - 8)x + 7 = -9x + 7.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a parenthesis.

Front

What is the solution to the equation 22 + 2a = 37 + 6 + a?

Back

First, simplify the right side: 22 + 2a = 43 + a. Subtract a from both sides: 22 + a = 43. Subtract 22: a = 21.

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value for all values of the variable(s). For example, 9(5c + 4) is equivalent to 45c + 36.