Equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you solve an equation with variables on both sides?

Back

1. Simplify both sides of the equation. 2. Move the variable terms to one side and constant terms to the other. 3. Isolate the variable.

Front

What does it mean for two expressions to be equal?

Back

It means that the values of the expressions are the same for certain values of the variable(s).

Front

If 10h = 5h + 7, how do you isolate h?

Back

Subtract 5h from both sides: 10h - 5h = 7, which simplifies to 5h = 7, then divide by 5.

Front

What is the first step in solving 4.6 + 1.2t = 54.6 - 0.8t?

Back

Combine like terms by adding 0.8t to both sides: 4.6 + 1.2t + 0.8t = 54.6.

Front

What is the significance of the constant in a linear equation?

Back

The constant represents a fixed value that shifts the graph of the equation up or down.

Front

How do you interpret the slope in a real-world context?

Back

The slope represents the rate of change between two quantities, such as cost per mile or gallons per minute.

Front

What is the solution to the equation 10h = 5h + 7?

Back

h = 7/5 or 1.4 hours.

Front

In the context of the taxi problem, what does the equation 3 + 1.5m = 30 represent?

Back

It represents the total cost of the taxi ride, where 3 is the base fare and 1.5m is the cost per mile.

Front

How do you find the number of pounds for Company A and Company B to cost the same?

Back

Set the cost equations equal: 7.25 + 0.20p = 5.15 + 0.30p and solve for p.