Equations & Inequalities Review

Front

What is an equation?

Back

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

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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 does it mean to solve an inequality?

Back

To solve an inequality means to find the range of values for the variable that make the inequality true.

Front

What is the first step in solving the equation 2x + 10 = 100?

Back

The first step is to isolate the variable by performing inverse operations, typically starting with subtraction.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations (addition, subtraction, multiplication, or division) to get the variable alone on one side of the equation.

Front

What is the solution to the equation 4 - 6x - 2 = -2(3x - 1)?

Back

The solution is infinitely many solutions, indicating that the equation is an identity.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What is the solution to the inequality 7x + 1 > 22?

Back

The solution is x > 3.

Front

What is the solution to the inequality 2x < -3x + 15?

Back

The solution is x < 3.