Solving Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to solve an equation?

Back

To solve an 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 -8 + 5x - 2 = 20?

Back

Combine like terms on the left side: -8 - 2 = -10, so the equation becomes 5x - 10 = 20.

Front

How do you isolate the variable in the equation 5x - 10 = 20?

Back

Add 10 to both sides to get 5x = 30, then divide by 5 to find x = 6.

Front

What is the solution to the equation 32 - 7x = -6(x + 3)?

Back

The solution is x = -50.

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 -6(x + 3)?

Back

Multiply -6 by both x and 3: -6x - 18.

Front

What is the solution to the equation 6(5x - 3) + 2 = 14?

Back

The solution is x = 1.

Front

What is the first step in solving the equation 7x - 3x - 8 = 24?

Back

Combine like terms: 4x - 8 = 24.

Front

How do you isolate x in the equation 4x - 8 = 24?

Back

Add 8 to both sides to get 4x = 32, then divide by 4 to find x = 8.