Solving Equations and Inequalities

Front

What is an equation?

Back

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

Front

How do you isolate a variable in an equation?

Back

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

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 an inequality?

Back

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

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign means changing 'greater than' to 'less than' (or vice versa) when multiplying or dividing both sides by a negative number.

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 side of the number line.

Front

What is the first step in solving the equation 7x + 6 + 2x = 60?

Back

Combine like terms to simplify the equation: 9x + 6 = 60.

Front

What is the solution to the equation 18 = 3b?

Back

b = 6.