Algebraic Manipulation Worksheets With Answers - Craven Community College (Page 2 of 29) in pdf

Algebraic Manipulation Worksheets With Answers - Craven Community College Page 2

QUATIONS AND

NEQUALITIES

Simplifying Algebraic Expressions

Simplifying generally means creating equivalent expressions that contain fewer additions and or

multiplications. To simplify algebraic expressions, combine like terms by adding their coefficients and

keeping the variable parts the same. To simplify expressions containing parentheses, remove all

parentheses and combine like terms. Remember to work problems containing parentheses from the inner

most set outward.

Example:

-(X-2Y) – 3(4X + Y)

Distribute constants and signs

-X – (-2Y) –3(4X) –3(Y)

Perform all multiplications

-X – 12X + 2Y – 3Y

Group like terms

-13X – Y

Solving Linear Equations

The solution to an equation is a number that, when substituted into the equation for the variable, results in

a true equation. Solving the equation means finding all such numbers. The general method of solving an

equation is to replace the given equation with simpler and simpler equations until an equation of the form

variable=constant occurs. The constant is then called the solution of the equation.

The two properties that are used to form these simpler equations are The Additive Property of Equations

and The Multiplicative Property of Equations.

The Additive Property of Equations: Adding (or subtracting) the same quantity to both sides of an

equation will not change the solution set of the equation.

Example 1:

X – 8 = 3

X – 8 + 8 = 3 + 8

Add 8 to both sides

X = 11

The Multiplicative Property of Equations: Multiplying (or dividing) both sides of an equation by the same

nonzero number will not change the solution set of the equation.

Example 2:

5X = 27

Divide both sides by 5

X = 27

Anytime more than one property is used, always use the addition property before the multiplication

property.

Algebraic Manipulation Worksheets With Answers - Craven Community College Page 2