Solving Equations with Variables on Both Sides

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What is the definition of an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you isolate a variable in an equation?

Back

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

Front

What is the first step in solving the equation x + 2 = x + 4?

Back

The first step is to subtract x from both sides to simplify the equation.

Front

What does 'less than' mean in mathematical terms?

Back

'Less than' indicates that one quantity is smaller than another, represented by the symbol '<'.

Front

How can you represent a real-world scenario using an inequality?

Back

You can represent a real-world scenario using an inequality by defining a situation where a quantity must not exceed a certain limit, such as budget constraints.

Front

What is the solution to the equation -15v - 40 = 23 - 8v?

Back

The solution is v = -9.

Front

What is the process for solving the equation -(8n - 2) = 3 + 10(1 - 3n)?

Back

First, distribute the negative sign and the 10, then combine like terms and isolate n.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the significance of the shipping fee in the T-shirt ordering scenario?

Back

The shipping fee adds a fixed cost to the total expense, which must be considered when determining how many T-shirts can be ordered within a budget.