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

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

How do you solve a one-variable equation?

Back

To solve a one-variable equation, isolate the variable on one side of the equation using inverse operations.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to manipulate an equation so that the variable is alone on one side of the equation.

Front

What is the solution to the equation 2x - 14 = 6?

Back

x = 10.

Front

How do you check if a solution is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the purpose of using variables in equations?

Back

Variables represent unknown values that can change, allowing us to express general relationships and solve problems.

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 graphs as a straight line.

Front

What does it mean to have a solution to an inequality?

Back

A solution to an inequality is a value or set of values that makes the inequality true.

Front

How do you graph an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side of the circle.