Clark S Final Project

Solving equations resource math year 1

final project

Algebraic Equation-

x+3=6

X+5=10

An algebraic equation is an equation that includes one or more variables

Algebraic expression-

• An algebraic expression is made up of the signs and symbols of algebra.

Functions-What is a What is a function?function?

A rule that establishes a A rule that establishes a relationship between two quantitiesrelationship between two quantities

What is What is function function form?form?

When a function is written so that When a function is written so that one of its variables in isolated on one of its variables in isolated on one side of the equation.one side of the equation.

1-step equation-

ADDITION-x + 4 – 4 = -12 –4      x = -16          ?

SUBTRACTION-d – 8 + 8 = -15 + 8      d = -7            ?

MULTIPLICATION-4c   (-4) = 44  (-4)      c = -11          ?

DEVISION-8 x f  8 = -4 x 8       f = -32          ?

To solve one-step equations use the inverse operation.      Addition is the inverse of subtraction and vice versa.      Multiplication is the inverse of division and vice versa

2-Step equation-

3h + 4 = 16

Examples-

2c - 7 = 21

k/4 + 9 = 21

m/3 - 5 = 22

2/3b + 7 = 21

3/4p - 4 = 25

Two-Step Equations are actually one-step

equations done twice.

If you can solve one-step addition or subtractions equations and one-step division or multpication equations,

then you can solve two-step division or multipication equations.

Absolute Value-Always a positive number, refers to the distance of a number from 0, the distances are positive.

|x + 1|  =  2

1.1. DistributeDistribute

2.2. Combine Like TermsCombine Like Terms

3.3. Move Variable to One SideMove Variable to One Side

4.4. Undo + or –Undo + or –

5.5. Undo Undo × or ÷× or ÷

1) Undo addition or subtraction outside of absolute value.

2) Undo multiplication or division outside of absolute value.

3) Set expression inside absolute value equal to the given value and its opposite.

4) Solve for variable using steps for solving equations.

Inequalities-Simple steps for solving Simple steps for solving

inequalities-inequalities-1.Distribute1.Distribute

2.Combine like terms2.Combine like terms3.Move the variable to one side3.Move the variable to one side4.Undo addition or subtraction4.Undo addition or subtraction

5.Undo multiplication or division 5.Undo multiplication or division (if mult. or div. by a neg. (if mult. or div. by a neg.

change sign)change sign)

The symbols < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to)

• Solve and Solve and graph each graph each inequality.inequality.

• 2x + 1 > 132x + 1 > 13

• 15 > 6 – 3x15 > 6 – 3x