Solving Algebraic Equations

Front

What is an algebraic equation?

Back

An algebraic equation is a mathematical statement that shows the equality of two expressions, typically involving variables and constants.

Front

What does it mean to solve an algebraic equation?

Back

To solve an algebraic equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation 7w + 3 = 5w + 9?

Back

The first step is to isolate the variable by moving all terms involving 'w' to one side and constant terms to the other side.

Front

Solve: 7w + 3 = 5w + 9

Back

w = 3

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you apply the distributive property to 4 = 2(x + 3)?

Back

You distribute 2 to both x and 3, resulting in 4 = 2x + 6.

Front

Solve: 4 = 2(x + 3)

Back

x = -1

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve.

Front

Solve: 8v - 4(v + 8) = 8

Back

v = 10

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to manipulate the equation so that the variable is on one side by itself.