Writing Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to solve for the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to 'solve an equation'?

Back

To find the value of the variable that makes the equation true.

Front

What is the first step in solving an equation with variables on both sides?

Back

Combine like terms and move all variable terms to one side of the equation.

Front

If 4x + 0.25 = 4.5x, how do you solve for x?

Back

Subtract 4x from both sides: 0.25 = 0.5x, then divide by 0.5 to find x = 0.5.

Front

What is the significance of the head start in the racing problem?

Back

The head start affects the distance each runner has to cover, influencing the equation set up to find when they meet.

Front

In the equation 400 + 75x = 1,000 - 25x, what do the terms represent?

Back

400 represents Celebrity A's initial followers, 75x represents followers gained over x days, 1,000 represents Celebrity B's initial followers, and -25x represents followers lost over x days.

Front

How do you determine when two linear equations are equal?

Back

Set the equations equal to each other and solve for the variable.

Front

What does the variable 'x' typically represent in these equations?

Back

The variable 'x' usually represents time, such as hours or weeks, in application-based problems.

Front

What is the importance of understanding the context of a problem?

Back

Understanding the context helps in setting up the correct equation and interpreting the results meaningfully.