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Solving Linear Equations
Transcript of Solving Linear Equations
Property Solving equations with variables on both sides Solving equations
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