8.17 - Modeling Equations

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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.

Front

What does it mean to model a situation with an equation?

Back

Modeling a situation with an equation means creating a mathematical representation of a real-world scenario using variables and constants.

Front

What is the solution to the equation X - 3 = 9?

Back

The solution is X = 12.

Front

How can you check if an equation is correct?

Back

You can check if an equation is correct by substituting the solution back into the original equation to see if both sides are equal.

Front

What is the significance of coefficients in an equation?

Back

Coefficients are the numerical factors that multiply the variables in an equation, determining the rate of change.

Front

What does the equation 2C = 8 represent in terms of solving for C?

Back

To solve for C, divide both sides by 2, resulting in C = 4.

Front

What is the first step in solving the equation 3x = 6?

Back

The first step is to divide both sides by 3, resulting in x = 2.

Front

How do you solve the equation 3x - 4 = x + 2?

Back

First, combine like terms: 3x - x = 2 + 4, which simplifies to 2x = 6. Then divide by 2 to find x = 3.

Front

What is the process to solve x + 18 = 2x + 6?

Back

Subtract x from both sides to get 18 = x + 6, then subtract 6 from both sides to find x = 12.