Nov. 13 - 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 and constants, and is often written in the form 'A = B'.

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, often written using symbols like >, <, ≥, or ≤.

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 the solution to the equation 2x + 3 = 7?

Back

x = 2.

Front

What is the solution to the inequality 3x - 5 < 4?

Back

x < 3.

Front

What is a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents an unknown value in an equation or expression.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation forms a straight line when graphed and has no variables raised to a power greater than one, while a nonlinear equation can form curves and has variables raised to powers greater than one.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves shading a region of the graph that represents all the possible solutions to the inequality, using a dashed line for < or > and a solid line for ≤ or ≥.

Front

What is the purpose of using parentheses in equations?

Back

Parentheses are used in equations to indicate which operations should be performed first, following the order of operations.

Front

What is the order of operations in mathematics?

Back

The order of operations is a set of rules that dictates the sequence in which calculations are performed: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.