simplifying expressions and solving equations
DESCRIPTION
Simplifying Expressions and Solving Equations. Mr. K’s Seven Steps for Solving Equations. 1. Distribute. Example: Use the distributive property. 2. Combine Like Terms on Same side of the equals sign. 3. Collect all variables on one side of the equals sign by + or -. - PowerPoint PPT PresentationTRANSCRIPT
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Simplifying Expressions and
Solving Equations
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Mr. K’s Seven Steps for Solving
Equations
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1. DistributeExample: Use the distributive property.
5( 1) 2( 4) 6
5 5 2 8 6
x x
x x
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2. Combine Like Terms on Same side of the equals sign
8 65 5 2
5 5 42 1
x x
x x
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3. Collect all variables on one side of the equals sign by + or -.
5 5 2 14
5 5 2 14
2
5 4
2
3 1
x
x
x
x
x
x
x
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4. Collect all constants on one side of the equals sign by + or -.
5
5 14
3
3
9
5
x
x
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5. Divide out the coefficient of the variable to isolate the variable.
3
3 9
3 9
93
3
x
x
x
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6. Simplify fractions if needed.
3
9
3
x
x
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7. Check your answer Mr. K’s way!
5 1 2 4 6
5 1 2 4 6
5 4 ?2 7 6
20 ? 14 6
20 20
3
3
x x
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What is an Additive Inverse?
• When using addition, and two values are combined, their sum is …..
• ZERO
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What is the Additive Inverse?
1. 8
2. 6
3.
4. - 5
5.
1
2
2
3
1
2
8
5
2
3
6
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Vocabulary• Equation– A mathematical statement that
two expressions are equal (has an equal sign)
• Solution of an Equation– Value of the variable that
makes the statement true
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Finding Solutions
• In order to find solutions we must, Isolate the Variable
• A variable is ISOLATED if it appears by itself on one side of the equation and not at all on the other side of the equation
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Solving Expressions• In order to solve any mathematical
expression we must always follow the order of operations
•PEMDAS• P – Please Parentheses• E – Excuse Exponents• M – My Multiply• D – Dear Divide• A – Aunt Add• S – Sally Subtract
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Solving Variable Equations
• In order to Isolate the variable, we sometimes need to move terms in the equations
• REMEMBER– When combining terms on the same side
of the EQUAL SIGN, you keep the SAME sign of the terms and just add them together
– We only use the OPPOSITE sign when we have to cross the equal sign
– This is because we are removing it from one side of the equal sign and adding it to the other side of the equal sign
4 5 2 1 3x y x y
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Moving Terms
• First look at the problem and decide which operations you have and do you have to move them across an equal sign
• If you do we must do the Inverse Operation in reverse order of the Order of Operations
Inverse Operations
Operation Inverse Operation
Addition Subtraction
Subtraction Addition
Multiplication Division
Division Multiplication
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Examples
10 4x
8 2b
7 9x
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Signs When Multiplying and Dividing
• Rules–Multiply
– Divide
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Examples
45
k
1.53
m
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Examples
7 56x
535
9v
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Homework
• Worksheet