Algebra is the branch of mathematics in which letters are used to represent numbers (unknowns) in expressions and equations.

An algebraic expression is a mathematical phrase that contains one or more numbers, one or more letters (variables), and one or more arithmetic operations. The letters stand for numbers that are unknown.

An unknown is a number we do not know,  in an equation is the variable to be solved.

Parentheses are used to group parts of an algebraic expression.  Example:   Twice the sum of a number and 5 ,       2(x+5)

An algebraic equation is statement of the equality of two expressions   (always include an equal sign).   Example:   3x + 4 = 10

An Equation is like a balance scale.  Everything must be equal on both sides. The task is to isolate the letter on one side of the equation or the other. Leave a positive variable in the result.

3x+1 = x+5

We can add or subtract the same amount on both sides of the equation; we can multiply or divide the same amount on both sides of the equation; and we can swap the expressions on both sides of the equation.

In algebra, we avoid using the multiplication sign (×), so that is not mistaken for the variable X. Multiplication is either indicated by a centered dot ( · ), by placing a number and a letter or by  parentheses.

Examples:

Twice a number                   2x

5 times a number                     5x

A number multiplied by 12       12x

The product of a number and 12     12x

Five times the sum of a number and 2         5(x+2)

The sum of twice a number and three times the number minus 6       (2x+3)(x-6)

 

A linear equation is an equation that gives a straight line when plotted on a graph.

• Standard Form

 Ax + By = C

where x and y are variables and A, B, and C are integers

• Slope-Intercept Form

y = mx + b

where m is the slope of the line and b is its y-intercept.

• Point-Slope Form

y − y1 = m(x − x1)

where m is the slope of the line and (x₁, y₁) are the coordinates of a given point on the line.

All the forms of a linear equation are equivalent.

If the highest exponent of the variables of an equation is 1, then the given equation is called a first-degree equation. Example: Y = 2X + 5

The graph of an equation of the first degree is a straight line.

A linear equation can be either proportional or non-proportional.

A proportional relationship is a linear equation with slope m that goes through the origin (0,0).    The constant b = 0 in the slope-intercept form.

y= mx

 

 

Solving One-Step Equations

 

AL03       Solving Equations (form ax + b = c ) 1

AL05       Solving Equations (form ax + b = c ) 2

AL06       Solving Equations (form ax + b = c ) 3

AL07       Solving Equations (form ax + b = c ) 4

AL14       Solving Equations (form ax + b = c ) 5

AL04       Solving Equations (form ax + b = c ) including negative values

AL16       Solving Equations by Addition and Subtraction 1

AL18       Solving Equations by Addition and Subtraction 2

 

AL08       Solving Equations with Variables on Both Sides 1

EQ01       Solving Equations with Variables on Both Sides 2

EQ02       Solving Equations with Variables on Both Sides 3

EQ03      Solving Equations with Variables on Both Sides 4

EQ04     Solving Equations with Variables on Both Sides 5

EQ05     Solving Equations with Variables on Both Sides 6

EQ06      Find_Slope

EQ07      Slope 2 point

EQ08      Slope

EQ09      Slope2

EQ10      K_From_Equation

EQ11      K_From_Graph

EQ12      K_From_Table

EQ13      K_Tables

Linear Equation Graph_(Help)

Properties_of_the Equality (Help)