Basic Algebra

Grade: 9th

Gustavo MirandaLRC 320

VocabularyExpressions:• Don’t contain an “=” sign• Contain variables• Values are substituted into variablesVariables:• Represented as letters, i.e. “x”Equations:• Also contain variables• Want to solve for specified variable• Contain an “=” sign

Evaluating Basic Expressions

• When evaluating, we want to plug in our given value into the variable and simplify by doing the indicated operation.

Basic Expression:

Ex:x + 5; when x = 2

Evaluating Advanced Expressions

• For advanced expressions, we want to combine like terms so that the expression becomes simpler and easier to evaluate.

Advanced Expression:Ex: Want this expression to be

simplified to:

x + 12 – 10x - 30; -9x – 18; when x = 3When x = 3

Examples for Evaluating Expressions

Ex: Evaluate the expression. x – 5; when x = 10

Solution: x – 5 (plug in given value for x)= 10 – 5= So, the solution to the

expression is 5.

Ex: Evaluate the expression.

2x + 5 – 3x + 10; when x = 2

Solution:

2x + 5 – 3x + 10 (Simplify terms with x)

= -1x + 5 + 10 (Now simplify constants)

= -1x + 15 (Plug in value for x)

= -1(2) + 15 (Simplify)

= -2 + 15

= 13, solution is 13

Solving Basic Equations

• With equations, they are expressions that are equal to a number.

• The goal with equations is to solve for a variable that contains a number for its solution.

Ex: (Basic equation) x + 3 = 10

Solving Advanced Equations

• With advanced expressions we wanted to simplify first; the same process is done with equations with more terms.

Ex: Solve for x. Want a simplified equation. x + 3 – 3x = 15 -2x + 3 = 15

Examples for Solving EquationsEx: Solve for x. x + 5 = 10

Solution: x + 5 = 10 (Subtract 5 from both sides of equation)

- 5 -5

So, x = 5

Ex: Solve for x. x - 5 - 3x - 1 = 9

Solution:

x – 5 – 3x – 1 = 9 (combine like terms)

-2x – 6 = 9 (Add 6 to both sides of equation)

+ 6 +6

-2x = 15 (Now divide -2 to both sides of equation) -2 -2

So, x = -15/2

Practice Exercises

Evaluate the following expressions:1) 2x + 3; when x = 22) x – 3; when x = 103) 3x – 5x +1; when x = 3

Solve the following equations for x.a) x + 5 = 2b) 2x – 3 + x = 6c) 3x – 10 = 5

Solutions:1) 7 2) 7 3) -5 a) x = -3 b) x = 3 c) x = 5