Algebra I Unit 1: Solving Equations in One Variable.
-
Upload
noah-short -
Category
Documents
-
view
245 -
download
3
Transcript of Algebra I Unit 1: Solving Equations in One Variable.
Algebra I Unit 1: Solving Equations in One Variable
Unit 1: Learning Goal 1.4
• Students will solve one-, two- and multi-step equations using the properties of real numbers and the properties of equality to justify the steps including real-world situations; represent solution process using concrete models.
Unit 1: Learning Goal 1.4 – Essential Knowledge and Skills for
Students• The students will use problem solving, reasoning,
communication, connections and representation to:– Using the properties of real numbers and the properties of
equality, and solve equations.– Use concrete and pictorial models to represent and solve
equations– Justify the steps to the solutions using the properties of real
numbers and the properties of equality.– Demonstrate an understanding that equivalent equations have
the same solution.– Demonstrate and understanding that adding the same
quantity to each side of an equation produces an equivalent equation.
– Write equations that represent real-world applications and solve using appropriate methods.
– Math/write a verbal statement that describes a given equation.
Unit 1: Learning Goal 1.4Algebra I Standards: EA-4.7, EA-1.3, and EA-
1.6
• EA-4.7 – Carry out procedures to solve linear equations in one variable algebraically.
• EA-1.3 – Apply algebraic methods to solve problems in real world contexts.
• EA-1.6 – Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.
Solving Equations by using addition and subtraction
Solving Equations by using addition and subtraction
Solving Equations by using addition and subtraction
27 -0.8 8Note: that when you have a term such as – c = -27 such as the
one above. The variable actually has a coefficient of -1. Remember that the product of two negative numbers is positive
you can multiply each side of the equation by -1 so that your answer is c = 27.
Solving Equations by using addition and subtraction
Helpful Hints: •If the same number is added or subtracted to each side of an equation, then the result is an equivalent equation. Equivalent Equations have the same solution.
•To Solve an equation means to find all values of the variable that make the equation a true statement. One way to do this is to isolate the variable having a coefficient of 1 on one side of the equation. You can sometimes do this by using the Addition Property of Equality.
•Isolating Variables – when isolating variables it does not matter whether the variable ends up on the right side or the left side of the equation. For example, the solution of 8 = 15 + z is still -7, even though the final step may be -7 = z.
Solving Equations by using addition and subtraction
Click here to try and electronically balance equations
Solving Equations by using multiplication and division
Solving Equations by using multiplication and division
Solving Equations by using multiplication and division
6y/6 = 54/6y = 9
-7d/ -7 = -84/-7d = 12
22b/22 = 176/22b = 8
2.4f/2.4 = 21.6/2.4f = 9
Solving Equations by using multiplication and division
(-6)(p/-6) = (7/12)(-6)p = -3 1/2
Change – 2 1/3 into – 7/3, which
is an improper fraction (-3/7)(-7/3q) = (21)(-3/7)
q = -9
Solving Multi-Step Equations
Solving Multi-Step Equations
Solving Multi-Step Equations
10 – 7p = -18-10 -10 -7p = -28 -7p / -7 = -28 / -7 p = 4
- 1.9r + 9.3 = 15 - 9.3 = -9.3 -1.9r = 5.7 -1.9r / -1.9 = 5.7/-1.9 r = -3
Solving Multi-Step Equations
(4)- 6 = [(-2n-3)/4](4)-24 = -2n-3-3 -3
-21/ -2 = - 2n/-2n = 10 1/2
(5)(t / 5 – 4)= - 10(5) t – 20 = -50
+ 20 = + 20 t = -30
Solving Equationswith variable on each side
Solving Equationswith variable on each side
Solving Equationswith variable on each side
Steps for solving Equations:Steps for solving Equations:Step 1: Use the Distributive Property to remove the grouping symbols.Step 2: Simplify the expressions on each side of the equals sign.Step 3: Use the Addition and/or Subtraction Properties of Equality to get the variables on one side of the equals sign and the numbers without variables on the other side of the equals sign.Step 4: Simplify the expression on each side of the equals sign.Step 5: Use the Multiplication or Division Property of Equality to solve.
•If the solution results in a false statement, there is no solution of the equation.•If the solution results in an identity, the solution is all numbers.
Solving Equationswith variable on each side
18 = 2n - 9
27 / 2 = 2n /2n = 13 1/2
+ 9 = + 9
18 + 2n = 4n – 9- 2n = - 2n
1 – 2.7 y = y
1/3.7 = 3.7y/3.7y = 1/3.7 or .27
+ 2.7y = + 2.7y
10 - 2.7y = y + 9- 9 = - 9
Solving Equationswith variable on each side
19.4 c – 2.4 = 6.4
19.4 c/19.4 = 8.8/19.4c = 8.8/19.4 or 0.45
+ 2.4 = + 2.4
11.1c – 2.4 = -8.3c + 6.4+ 8.3 c = + 8.3 c
3 = 12x + 8
- 5/12 = 12x/12x = -5/12
- 8 = - 8
3 – 4x = 8x + 8+ 4x = 4x
Work Cited
• Carter, John A., et. al. Glencoe Mathematics Algebra I. New York: Glencoe/McGraw-Hill, 2003.
• Greenville County Schools Math Curriculum Guide