Classroom Finding a Solution from a Giver.

Write the word statement as an equation. Use x as the variable. Then find all solution of the equation from the set (0, 2, 4, 6, 8, 10). Three times a number is subtracted from 21, giving 15. 21 —3x = 15 Substitute each of the given numbers. The solution is 2, because 21 — 3(2) = 15.

Decide whether each equation has the given number as a solution. a. 8p — 10 5; 2

Equations and Expressions An expression is a phrase that represents a number.  4x + 5 (expression)

An equation is a sentence—it has something on the left side, an = symbol, and something on the right side.  4x + 5 = 9 (equation)

Identify Solutions An equation is a statement that two algebraic expressions are equal. An equation always includes IA equality symbol, = .
Examples of equations: x+4=11 2y=16 4p+1=25—p
z.2 = 4
3 1 71x+2=°
4(m —0.5)=2m

To solve an equation means to find the values of the variable that make the equation true. Such a value of the variable is a solution of the equation.
Classroom Deciding Whether a Number is a Solution

Identify Solutions
A set is a collection of objects. In mathematics, these objects are usually numbers. The objects that belong to a sct are its elements. They are written between braces I }. For example, the set containing the numbers (or elements) 1, 2, 3, 4, and 5 is writtcn as (1 , 2, 3, 4, 5).
One way of determining solutions is the direct substitution of all possible replacements. The ones that lead to true statements arc solutions.
Finding a Solution from a Given Set

Evaluating Algebraic Expressions Evaluate each expression for p 3.
a. 16p — 8
b. 2p’

Variables, Expressions, and Equations
I. Evaluate algebraic expressions, given values for the variables. 2. Translate word phrases to algebraic expressions. 3. Identify solutions of equations. 4. Identify solutions of equations from a set of numbers. 5. Distinguish between expressions and equations.

Evaluating Algebraic Expressions Evaluate each expression for x = 6 and y = 9. a. 4x + S Y b. 4x — 2y x +1

Using Variables to Write Word Phrases as Algebraic Expressions Write each word phrase as an algebraic expression using x as the variable.
a. A difference of 48 and a number. 48 — x
b. The product of 6 and a number 6x
c. 9 multiplied by the sum of a number and 5 9(x + 5) U
Identify Solutions

Definitions
A constant is a fixed, unchanging number. A variable is a symbol. ustally a letter such as x, y, or 1, used to represent any unknown number.
An algebraic expression is a sequence of constants, variables, operation symbols, and/or grouping symbols (such as parentheses) formed according to the rules of algebra. For example: x + 5, 2m — 9, 8p2 + 6(p – 2)
In 2m — 9, the 2m means “2 times in.- 0======11.11