Modeling and Solving Algebraic Equations

Front

What is an algebraic equation?

Back

An algebraic equation is a mathematical statement that shows the equality of two expressions, typically involving variables and constants, such as x + 3 = 9.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value of the variable that makes the equation true.

Front

What is the first step in solving the equation x - 3 = 9?

Back

Add 3 to both sides to isolate x: x = 12.

Front

How do you model a situation with an equation?

Back

You translate a real-world scenario into a mathematical equation using variables to represent unknown quantities.

Front

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

Back

Isolating the variable allows you to find its value by getting it alone on one side of the equation.

Front

What does the equation 2x + 4 = 10 represent?

Back

It represents a situation where twice a number (x) plus 4 equals 10.

Front

How can you check if your solution to an equation is correct?

Back

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

Front

What is the solution to the equation 3x - 8 = 3?

Back

Add 8 to both sides to get 3x = 11, then divide by 3 to find x = 11/3.

Front

What does the equation t + 4 = 7 mean in a real-world context?

Back

It means that if you add 4 to a number t, the result is 7.

Front

What is the significance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides have the same value.