Solving Equations with Variables on Both Sides

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing 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 a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents an unknown value in an equation.

Front

What is the first step in solving the equation 12x - 15 = 3(2x + 3)?

Back

Distribute the 3 on the right side to get 12x - 15 = 6x + 9.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the solution to the equation 3c + 5 = 23?

Back

c = 6.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What is the solution to the equation 14 - 2(3p + 1) = 6(4 + p)?

Back

p = -1.

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

What is the first step in solving the equation 2a - 4(a - 5) = 10?

Back

Distribute -4 to a and -5.