Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to 'combine like terms'?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, in the expression 3x + 2x, you can combine them to get 5x.

Front

What is the purpose of isolating the variable in an equation?

Back

Isolating the variable means getting the variable alone on one side of the equation to solve for its value.

Front

What is the first step to solve the equation 5k + 6 = -9?

Back

Subtract 6 from both sides of the equation to isolate the term with the variable.

Front

How do you simplify the expression 3x - 5x?

Back

Combine the like terms to get -2x.

Front

What is the result of simplifying 3x + 2x?

Back

The result is 5x.

Front

What is the first step to solve the equation 3x + 6 = 10 + 3x + 4x?

Back

Combine like terms 3x and 4x on the same side of the equation.

Front

What is the next step to solve the equation 3x - 5 = 7?

Back

Add 5 to both sides of the equation.

Front

What does it mean to 'subtract from both sides' of an equation?

Back

It means to take the same number away from both sides of the equation to maintain equality.

Front

What is the solution to the equation 2x + 4 = 12?

Back

Subtract 4 from both sides to get 2x = 8, then divide by 2 to find x = 4.