Basic Algebra Grade 9 th Gustavo Miranda LRC

Basic Algebra Grade: 9 th Gustavo Miranda LRC 320

Vocabulary Expressions: • Don’t contain an “=” sign • Contain variables • Values are substituted into variables Variables: • 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 – 10 x - 30; When x = 3 -9 x – 18; when x = 3

Examples for Evaluating Expressions Ex: Evaluate the expression. x – 5; when x = 10 Ex: Evaluate the expression. 2 x + 5 – 3 x + 10; when x = 2 Solution: x – 5 (plug in given value for x) = 10 – 5 = So, the solution to the expression is 5. 2 x + 5 – 3 x + 10 (Simplify terms with x) = -1 x + 5 + 10 (Now simplify constants) = -1 x + 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. x + 3 – 3 x = 15 Want a simplified equation. -2 x + 3 = 15

Examples for Solving Equations Ex: 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 - 3 x - 1 = 9 Solution: x – 5 – 3 x – 1 = 9 (combine like terms) -2 x – 6 = 9 (Add 6 to both sides of equation) + 6 +6 -2 x = 15 -2 (Now divide -2 to both sides of equation) -2 So, x = -15/2

Practice Exercises Evaluate the following expressions: 1) 2 x + 3; when x = 2 2) x – 3; when x = 10 3) 3 x – 5 x +1; when x = 3 Solve the following equations for x. a) x + 5 = 2 b) 2 x – 3 + x = 6 c) 3 x – 10 = 5 Solutions: 1) 7 2) 7 3) -5 a) x = -3 b) x = 3 c) x = 5