Algebra 1 notes

What is an Equation?

A mathematical statement showing that two expressions are equal.

What is a Variable?

A letter or symbol representing a value that can change.

What is a Constant?

A value that remains fixed.

What is a Coefficient?

A number multiplied by a variable in an algebraic expression.

What are Terms?

Parts of an expression or equation, separated by + or - signs.

What are Like Terms?

Terms with the same variables raised to the same powers.

What does Combining Like Terms do?

It simplifies an expression by grouping like terms together.

What is an Inequality?

A mathematical sentence comparing two expressions using symbols like

What is the Domain?

The set of all possible input values (x-values) for which a function is defined.

What is the Range?

The set of all possible output values (y-values) of a function.

What is an Expression?

A relationship or expression involving one or more variables.

What is a Solution?

A value that, when substituted for a variable, makes an equation true.

What does Solving entail?

The process of finding the value(s) that satisfy an equation.

What is a Base in mathematics?

A number or expression raised to a power.

What is an Exponent?

A quantity representing the power to which a number or expression is raised.

What is an Algebraic Expression?

A mathematical phrase involving numbers, variables, and operations.

What is a Comparison?

A statement indicating how two numbers or expressions relate.

What is Prime Factorization?

The representation of a number as a product of its prime factors.

What is a Linear Graph?

A straight-line graph representing a linear equation.

What is a Linear Function?

A function whose graph is a straight line.

What is Slope-Intercept Form?

A function written as f(x) = mx + b, where m is the slope and b is the y-intercept.

How is Slope calculated?

As the change in y divided by the change in x.

What is the Y-Intercept?

The point where a line crosses the y-axis, represented as (0, b).

What is the first step in solving the linear equation 2x + 3 = 7?

Subtract 3 from both sides to get 2x = 4.

How do you find the value of x in the equation x^2 - 4x + 4 = 0?

Factor it as (x - 2)(x - 2) = 0 and solve for x = 2.

What is the process to solve the equation with fractions: (x/2) + (1/3) = 1?

Find a common denominator, multiply by it, and solve the resulting equation.

How do you solve the equation 3(x - 2) = 9?

Distribute and isolate x, resulting in x = 5.

What is the solution for the equation x^3 = 8?

Take the cube root of both sides, resulting in x = 2.

How do you setup equations for |x - 1| = 2?

Set up two equations: x - 1 = 2 and x - 1 = -2.

What is the form of a linear equation in two variables?

It can be represented as 2x + y = 5.

How do you find the slope and y-intercept from the equation f(x) = -3x + 4?

The slope is -3 and the y-intercept is (0, 4).