Solving Linear Equations with Variables on Both Sides

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 solve a linear equation with variables on both sides?

Back

It means to find the value of the variable that makes the equation true, where the variable appears on both sides of the equation.

Front

How do you isolate a variable in a linear equation?

Back

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

Front

What is the first step in solving the equation 4k + 24 = 6k - 10?

Back

The first step is to move all terms involving k to one side of the equation and constant terms to the other side.

Front

What is the solution to the equation 2x + 1 = 2x - 1?

Back

There is no solution because the equation simplifies to 1 = -1, which is a contradiction.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation.

Front

How do you check if your solution to a linear equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 4( x + 2) = 16?

Back

The solution is x = 2.

Front

What is the importance of combining like terms in solving linear equations?

Back

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

Front

What is the result of the equation 4x - 5x + 9 = 5x - 9 after combining like terms?

Back

The equation simplifies to -x + 9 = 5x - 9.