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

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side. This often involves adding, subtracting, multiplying, or dividing.

Front

What does it mean to solve for x in an equation?

Back

Solving for x means finding the value of x that makes the equation true.

Front

What is the first step in solving the equation 3(5x + 10) + 10 = 6x - (x + 10)?

Back

The first step is to distribute the 3 on the left side of the equation.

Front

What is the solution to the equation 10 = 3x - 12?

Back

The solution is x = 22/3.

Front

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

Back

You can check your solution by substituting the value of x back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 2x + 5 = 12?

Back

The solution is x = 3.5.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable. It represents how steep the line is.

Front

What does the term 'like terms' mean in algebra?

Back

Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.

Front

What is the solution to the equation 7 - 5x = 12?

Back

The solution is x = -1.