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Unit 3
Solving Equations
Learning Goals• I can solve simple one and two step equations
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Unit 3: Solving Equations
• Relationships can be described by equations• You can create a table of values to determine
a pair of values that satisfies the equation.• A pair of values that satisfies the equation is
called a solution to the equation.• A complete graph of the equation would show
all possible solution pairs for the equation.
How do you find the solution to an equation?
Solving Polynomial Equations (1)
Success Criteria:
1. Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed to isolate the variable on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Solve: y + 7 = 16
Unit 3: Solving Equations
Solving Polynomial Equations (1)Success Criteria
1. Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.Left Side Right Side
CHECK
Solve: 14 = p - 2
Unit 3: Solving EquationsSolving Polynomial
Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Solve: 56 = 8m
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Solve: 10c – 7 = 53
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Solve: + 6 = 8
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Solve:
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Solve: 4x + 6 = 3x
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Left Side Right SideCHECK
Success Criteria1. Isolate the variable on one side
of the equation by adding, subtracting, multiplying, or dividing (get the variable by itself). Do the opposite: if 3 is being added to “x” subtract 3 to get “x” by itself. Remember SAMDEB.
2. Every step that is performed on one side of the equation MUST be performed on the other side of the equation to maintain equality.
3. Perform a “check” by substituting the values you found for the solution into the equation and ensuring that the left side equals the right side.
Mary works part time at a local coffee shop where she earns $9 per hour. She also babysits children in her neighbourhood and she charges $6 per hour. Mary is saving up to buy a new computer which will cost her $783. In order to earn the money for the computer, what combination of hours could Mary work at each job? Find 3 different combinations.
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Graph the relationship that represents the number of hours Mary would have to work at each job in
order to make $783.
Unit 3: Solving EquationsSolving Polynomial
Equations (1)
y
x
What are the intercepts?
What do they represent?
Unit 3: Solving Equations
Solving Polynomial Equations (1)
Practice
• Read Page 292 Example #1 and #2• Do Page 294 Q# 1 through 6 parts
“g” and “j”• Page 296 Q# 14 gjm, 15 adgj, 18beh,
19bdf* Do proper “CHECKS” for questions 1gj, 5gj, 15g, 18b, 19b *
Unit 3: Solving Equations
Solving Polynomial Equations (1)
