Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does 'combining like terms' mean?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

How do you isolate a variable in an 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 -12t + 10 + 32 = 78?

Back

The first step is to combine like terms: -12t + 42 = 78.

Front

What is the solution to the equation 4x + 14 + 4x = 38?

Back

The solution is x = 3.

Front

How do you solve for p in the equation 15 - 8p + 6.75p = 10?

Back

Combine like terms to get 15 - 1.25p = 10, then isolate p.

Front

What does it mean to 'subtract the constant' in an equation?

Back

Subtracting the constant means to remove the number that is not attached to a variable from both sides of the equation.

Front

What is the solution to the equation -12 = 10n - 40n + 3?

Back

The solution is n = 1/2 or 0.5.

Front

How do you solve the equation 1/2b + 8 - 10 = 6?

Back

First, simplify to get 1/2b - 2 = 6, then isolate b to find b = 16.

Front

What is the purpose of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation.