Solving Equations - Algebra 1

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one, and it can be written in the form ax + b = c.

Front

What is the solution set of an equation?

Back

The solution set is the set of all values that satisfy the equation.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can make the equation true.

Front

What is an example of an equation with no solution?

Back

An example is 2x + 1 = 2x + 3, which simplifies to 1 = 3, a false statement.

Front

What is an example of an equation with infinitely many solutions?

Back

An example is 2(x + 5) = 2x + 10, which simplifies to 10 = 10, a true statement for all x.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the equation 0.50x + 20 = 35?

Back

The first step is to subtract 20 from both sides to isolate the term with the variable.

Front

What is the significance of coefficients in an equation?

Back

Coefficients are the numerical factors that multiply the variables in an equation, affecting the slope and position of the line represented by the equation.