Solving Linear Equations Solving one step equations Using Addition and Subtraction Using Multiplication and Division The Distributive

Property Solving equations with variables on both sides Solving equations

with ratios/

fractions What do you know about solving linear equations (from Grade 8)? Do you know the following words? constant variable numerical

coefficient i.e. the x variable 'LIKE TERMS'

a term is an expression formed from the product of numbers &/0r variables (i.e. 3x, 2, 8r)

like terms have the same variables raised to the same exponent (i.e. -x and 2x, 3ab and 4.5ab) equation ex. 5, 1/2, 2.5 in the equation 3x + 2.5 = 6, Solving equations with

more than one step is a statement that two math expressions or numbers are equal.

(i.e. x + 2 = 5) represents an unknown number. a number that multiplies the variable (i.e. the number beside the variable) combine like terms in each expression:

A. 4x - 2x + 3 - 6

B. 4 - 3m + 4m - 2 + 5d a. add or subtract coefficients of like terms

= 2x - 3

b. = m + 5d + 2 2x + 3 = 5 8 = 4x + 6 -a + 9a = 10 12 + 2f = 4.5f y = -2 2x = 16 to solve an equation is to find

the value of the variable that makes

the statement true

(i.e. for x + 2 = 5 to be true, x must equal 3) Find r in the equation, 5 + r = 3

We need to isolate the variable to one side of the equation to find r. You can use:

opposite operations or by tranposing terms UNLIKE TERMS

have different variables or same variables with different exponents

(i.e. a, 3a, b, -c, 4x, 5.6z) opposite operations 'undoes' another operation.

- examples are: + and -, x and ÷

- also called inverse operations 5 + r = 3

5 - 5 + r = 3 - 5

r = -2 to bring a term from one side of the equation to the other with a change of sign 5 + r = 3

r = 3 - 5

r = -2 s + 5 = - 3

s + 5 - 5 = -3 - 5 s = -3 - 5

s = - 8 s = - 8 how would you solve this equation:

2x = 8 2x we can use a number line to answer the question:

2x = 8 the length of the curly bracket represents 2x so half of this length represents x. x x it shows that x = 4. substitute -8 into the original equation to check your answer:

left side = right side

s + 5 = -3

(s = -8) -8 + 5 = -3

-3 = -3

We need to use the inverse operations to solve one-step equations using multiplication and division. ex. 2x = 3/4 2 + 5 4

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# Solving Linear Equations

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