Solving Equations 1 step Equations 2 step Equations

Solving Equations 1 -step Equations 2 -step Equations MULTI-Step Equations

Definitions • Variable – A variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables. For example, we might say that s stands for the side-length of a square. We now treat s as if it were a number we could use.

Definitions • Expressions – An expression is a mathematical statement that may use numbers, variables, or both.

Expressions • • The following are examples of expressions: 2 x 3+7 2×y+5 2 + 6 × (4 - 2) z + 3 × (8 - z)

Definitions • Equation – An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Many word problems can easily be written down as equations with a little practice. Many simple rules exist for simplifying equations.

Equations • • The following are examples of equations: 2=2 17 = 2 + 15 x=7 7=x t+3=8 3 × n +12 = 100

Solution of an Equation • When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value.

Solution of an Equation • Example: • We say y = 3 is a solution to the equation 4 × y + 7 = 19, for replacing each occurrence of y with 3 gives us • 4 × 3 + 7 = 19 ==> • 12 + 7 = 19 ==> • 19 = 19 which is true.

Simplifying Equations To find a solution for an equation, we can use the basic rules of simplifying equations.

Rules 1)You may add any value to both sides of the equation. 3 x - 5 = 20 5 + 3 x + 5 = 20 + 5

Rules 2) You may subtract any value from both sides of the equation. This is best done by adding a negative value to each side of the equation. 2 x + 3 = 5 -3 + 2 x + 3 = 5 - 3

Rules 3) You may multiply both sides of the equation by any number except 0.

Rules 3) You may divide both sides of the equation by any number except 0. 3 x = 9

Teachers! Turn on your Student Response Systems Fast grade

SOLVE 3 x – 2 = 4 A. 2/3 B. 2 C. 6 D. 3

SOLVE -b + 6 = -11 A. -17 B. 5 C. -5 D. 17

SOLVE 1= +5 A. -24 B. 24 C. 48 D. -48

Practice

Practice • This can be confusing so rather than give you the answers, which sometimes do not help, please click on to Algebasics to HEAR and See how to do these problems. – Make sure to navigate to Section 2: Equations

Lesson 3 Solving for the Variable • Print and gather materials – Chapter 7 Section 1: Read pages 336 -37 and do problems in in the textbook page 338, 11 -25 odd. – Check answers in back of text. – Study guide page 57 in supplementary textbook. – Take Self-Test Quiz