chapter 4mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · 4.1d solve one-step addition and...
TRANSCRIPT
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Chapter 4
Equations and Inequalities
10/2017 LSowatsky 1
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4.1D Solve One-Step Addition and Subtraction Equations I can solve addition and subtraction equations.
LSowatsky 2 7.EE.4
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Solving Equations Using Addition or Subtraction: If a number has been added to
the variable, subtract that number from both sides of the equation.
If a number has been subtracted from the variable, add that number to both sides of the equation.
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Inverse operations: operations that ‘undo’ each other
LSowatsky 4
Solve 7 = 15 + c Solve -5 = z - 16
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Solving Equations Basics
When transforming equations (isolating the variable) – they
must remain balanced! Whatever you do to one side of the =
sign, you MUST do to the other side!
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Solution Steps Each time you apply a transformation to an equation, you are writing a solution
step. Solution steps may be written one below each other with the equal sign
aligned.
Survival tip: SHOW your solution steps – it makes checking your work
easier and your grade higher! This may not seem important now, but when
have you much more complex equations, you will need that skill.
Showing your work is NOT optional!!!!
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Example: solve and check your solution.
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Homework:
p.
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4.2B Solve One-Step Multiplication and Division Equations I can solve one-step multiplication and division
equations.
LSowatsky 9 7.EE.4
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Vocabulary:
Coefficient: the number that multiplies a variable
Formula: an equation that shows the relationship between certain quantities
LSowatsky 10
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Solving One-Step Equations
1) Use Inverse Operations to solve Operations that “undo” each other Multiplication is the inverse of division Division is the inverse of multiplication
2) Make sure variable is by itself 3) Check answer
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Solving Equations Using Multiplication or Division
If a variable has been multiplied by a nonzero number, divide both sides by that number.
If a variable has been divided by a number, multiply both sides by that number.
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3y = 261 To undo the multiplication by 3, divide 3 from both sides of the equal
sign.
3 3 y = 87
Check the solution.
3y = 261 Replace the variable
with your answer.
3(87) = 261 261 = 261
Example: Solve 3y = 261
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To undo the multiplication of -1 , divide both
sides by -1.
Example: Use the multiplication property of - 1
-w = 42
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More examples: Solve and Check
1) -5x=19 2) x/7=-12
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Using Formulas:
• The distance D that Ryan travels on his bike at a rate of 20 miles per hour for 4 hours is given by the equation . How far did re ride?
•
LSowatsky 16
204
d
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Homework:
p. 218 #9 – 25, 27
10/2017 LSowatsky 17
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4.2D Solve Equations with Rational Coefficients I can solve equations with rational coefficients.
LSowatsky 18 7.EE.4
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Vocabulary:
Reciprocals (aka multiplicative inverses):
two numbers with a product of 1
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Solve with Fractional Coefficients:
Multiply by the reciprocal to get the variable by itself
Example:
LSowatsky 20
36
4x
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Example: Solve and Check your solution.
LSowatsky 21
2 6
5 15x
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Solve with Decimal Coefficients:
Divide each side by the coefficient
Example: 0.75 = 3.75
LSowatsky 22
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Example: Solve and check your solution.
10 = 0.5x
LSowatsky 23
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Homework:
p. 224 #13 – 34, 36 - 38
10/2017 LSowatsky 24
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4.3B Solve Two-Step Equations
I can solve two-step equations
LSowatsky 25 7.EE.4, 7.EE.4a
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Things to Remember
Goal is to get the variable by itself.
Addition and Subtraction are inverse operations.
Multiplication and Division are inverse operations.
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Don’t Forget
Keep the equation balanced. Whatever you do to one side, you must do to the other.
This Photo by Unknown Author is licensed under CC BY-SA
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How to solve two-step equations:
“Undo” the operations in the reverse order of the order of operations.
For example: In order of operations we do multiplication or division first, then addition and subtraction. When solving an equation we do the opposite.
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Examples: Solve and check solution. 1) 3x + 2 = 33 2) -3c + 9 = 3
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More Examples: Solve and check solution 1) 2) -2y – 7 = 3 1
4 15
x
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Recap:
Undo the addition or subtraction first
Undo the multiplication or division second.
LSowatsky 31
Order of operations in reverse!
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Homework:
p. 233 #8 – 27, 29, 32
10/2017 LSowatsky 32
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4.3D Solve Equations with Variables on Each Side I can use the properties of equality to simplify and
solve equations with variables on each side.
LSowatsky 33 7.EE.4
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bkevil
Steps to Solve Equations with Variables on Both Sides
1) Combine like terms on both sides (if needed).
2) Get variable on one side of the equation
3) Solve 2 step equation by undoing what has been done to the variable.
4) check solution
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Example:3x – 2 = 2x + 1
LSowatsky 35
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Example: 2x – 9 = 5x + 3
LSowatsky 36 6/20/2011
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8x = x - 49
LSowatsky 37 6/20/2011
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Exit Ticket: Solve on scrap paper and turn in before you leave -18 + 3x = x - 6
LSowatsky 38
This Photo by Unknown Author is licensed under CC BY-SA
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Homework:
p. 238 #11 – 30, 34
10/2017 LSowatsky 39
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4.4B Solve Inequalities by Addition or Subtraction I can solve inequalities by using the addition and
subtraction properties of inequality.
LSowatsky 40 7.EE.4
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Solving an Inequality: Solving a linear inequality in one variable is much like solving a linear equation in one variable.
Isolate the variable on one side using inverse operations.
Add the same number to EACH side.
Solve using addition:
53x
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Solving Using Subtraction:
Subtract the same number from EACH side.
106 x
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Using Subtraction:
35x Graph the solution.
-5 -4 -3 -2 -1 0 1 2 3 4 5
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Using Addition:
-5 -4 -3 -2 -1 0 1 2 3 4 5
42 n Graph the solution.
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Example: Write an inequality and solve.
LSowatsky 45
Four more than a number is more than 13.
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Homework:
p. 247 #11 - 29
10/2017 LSowatsky 46
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4.4C Solve Inequalities by Multiplication or Division. I can solve inequalities by using the multiplication or
division properties of inequality.
LSowatsky 47 7.EE.4
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Solving Inequalities Using Multiplication:
Multiply each side by the same positive number.
32
1x
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Solving Inequalities Using Division:
Divide each side by the same positive number.
93 x
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Multiply or Divide by a Negative Number:
NOTE:
When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.
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Solving by multiplication of a negative #
Multiply each side by the same negative number and REVERSE the inequality symbol.
4 x Multiply by (-1).
4x
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Solving by dividing by a negative #
Divide each side by the same negative number and reverse the inequality symbol.
62 x
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Example: A plate weighs ¼ pound. A shelf can hold at most 20 pounds. Write and solve an inequality to find how many plates the shelf can hold.
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Homework:
p. 252 #14 – 38, 41
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Chapter Test
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