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Solving Equations
   Vocabulary words
Equation


A mathematical sentence that uses an equal sign
to show that two expressions are equal.

 X – 26 = 3 is an equation.




11/5/2012
                                                  2
Solution
The value that makes the equation true.


The solution to the problem
x-3 = 7 is 10.




solution
11/5/2012
                                          3
Inverse operations


Operations that “undo” each other.

The inverse operation of
addition is subtraction.




11/5/2012
                                     4
Multiplication property of equality
When you multiply each side of the equation by
the same non-zero number, it results in an
equivalent equation.
If I multiply 2/5 on one side of the
equation and multiply 2/5 on the
other side of the equation, I am
showing the Multiplication
property of equality.


 11/5/2012
                                                 5
Two-step equation
An equation that contains two different operations.

The equation 2x - 3 = 9 is a two-
step equation.




11/5/2012
                                                      6
Terms
The coefficients, variables and constants that
make up an equation.

In the expression
3x + 4y + 7 - 12 + 10x + 6y…
3x, 4y, 7, -12, 10x, 6y are all
terms.




 11/5/2012
                                                 7
Addition Property of Equality
When you add each side of the equation by the
same nonzero number, it results in an equivalent
equation.
If I add 4 to one side of the
equation and add 4 to the other
side of the equation, I am
showing the Addition property
of equality.


 11/5/2012
                                                   8
Coefficient
The number in front of a variable.

The coefficients in the expression
13x + 10y - 5 are 13 and 10

                    coefficient


                    =3b
     b      b   b
                     variable
11/5/2012
                                     9
Division Property of Equality
When you divide each side of the equation by the
same nonzero number, it results in an equivalent
equation.
If I divide by -3 on one side of the
equation and divide by -3 on the
other side of the equation, I am
showing the Division property
of equality.


11/5/2012
                                                   10
Equivalent Equations
Two equations that have the same solution.

The equations x + 10 = 20 and
X = 10 are equivalent
equations.




 11/5/2012
                                             11
Like terms
Terms that look alike involving variables and
constants.

In the equation
3x + 4y + 7 - 12 + 10x + 6y…
3x and 10x, 4y & 6y, 7 & -12 are
all like terms




11/5/2012
                                                12
Subtraction Property of Equality
When you subtract each side of the equation by
the same nonzero number, it results in an
equivalent equation.

If I subtract 4 on one side
of the equation and
subtract 4 on the other side
of the equation, I am
showing the Subtraction
property of equality.

11/5/2012
                                                 13
Variable
An unknown quantity that is represented by one of
the 26 letters of the alphabet.

In the equation 3x + 4 = 8, the x
is the variable.




11/5/2012
                                                14
11/5/2012
            15

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Vocabulary presentation equations

  • 1. Solving Equations Vocabulary words
  • 2. Equation A mathematical sentence that uses an equal sign to show that two expressions are equal. X – 26 = 3 is an equation. 11/5/2012 2
  • 3. Solution The value that makes the equation true. The solution to the problem x-3 = 7 is 10. solution 11/5/2012 3
  • 4. Inverse operations Operations that “undo” each other. The inverse operation of addition is subtraction. 11/5/2012 4
  • 5. Multiplication property of equality When you multiply each side of the equation by the same non-zero number, it results in an equivalent equation. If I multiply 2/5 on one side of the equation and multiply 2/5 on the other side of the equation, I am showing the Multiplication property of equality. 11/5/2012 5
  • 6. Two-step equation An equation that contains two different operations. The equation 2x - 3 = 9 is a two- step equation. 11/5/2012 6
  • 7. Terms The coefficients, variables and constants that make up an equation. In the expression 3x + 4y + 7 - 12 + 10x + 6y… 3x, 4y, 7, -12, 10x, 6y are all terms. 11/5/2012 7
  • 8. Addition Property of Equality When you add each side of the equation by the same nonzero number, it results in an equivalent equation. If I add 4 to one side of the equation and add 4 to the other side of the equation, I am showing the Addition property of equality. 11/5/2012 8
  • 9. Coefficient The number in front of a variable. The coefficients in the expression 13x + 10y - 5 are 13 and 10 coefficient =3b b b b variable 11/5/2012 9
  • 10. Division Property of Equality When you divide each side of the equation by the same nonzero number, it results in an equivalent equation. If I divide by -3 on one side of the equation and divide by -3 on the other side of the equation, I am showing the Division property of equality. 11/5/2012 10
  • 11. Equivalent Equations Two equations that have the same solution. The equations x + 10 = 20 and X = 10 are equivalent equations. 11/5/2012 11
  • 12. Like terms Terms that look alike involving variables and constants. In the equation 3x + 4y + 7 - 12 + 10x + 6y… 3x and 10x, 4y & 6y, 7 & -12 are all like terms 11/5/2012 12
  • 13. Subtraction Property of Equality When you subtract each side of the equation by the same nonzero number, it results in an equivalent equation. If I subtract 4 on one side of the equation and subtract 4 on the other side of the equation, I am showing the Subtraction property of equality. 11/5/2012 13
  • 14. Variable An unknown quantity that is represented by one of the 26 letters of the alphabet. In the equation 3x + 4 = 8, the x is the variable. 11/5/2012 14
  • 15. 11/5/2012 15