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 with variables on both sides?

Back

You can isolate a variable by moving all terms containing that variable to one side of the equation and constant terms to the other side.

Front

What is the first step in solving the equation 25 + x = 15 + 2x?

Back

Subtract x from both sides to simplify the equation.

Front

In the equation 3x = x + 10, how do you solve for x?

Back

Subtract x from both sides to get 2x = 10, then divide by 2 to find x.

Front

What does it mean for two expressions to be equal in an application problem?

Back

It means that the total costs or values represented by the expressions are the same under certain conditions.

Front

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

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the significance of the coefficients in an equation like 100 + 45x = 125 + 30x?

Back

The coefficients represent the rate of change or cost per unit, which affects how quickly the total cost increases.

Front

What strategy can be used to solve the equation 15 + 2.5x = 10 + 3x?

Back

Rearrange the equation to isolate x by moving all x terms to one side and constant terms to the other.

Front

What is a common mistake when solving equations with variables on both sides?

Back

A common mistake is forgetting to perform the same operation on both sides of the equation, which can lead to incorrect solutions.

Front

How do you interpret the solution of an equation in a real-world context?

Back

The solution represents the point at which two different scenarios or costs become equal, often indicating a break-even point.