This document defines key terms used in solving equations, including equation, solution, inverse operations, terms, coefficients, variables, equivalent equations, like terms, and properties of equality. It provides examples to illustrate each term and explains how operations like addition, subtraction, multiplication, and division can be used to solve equations while maintaining equivalency.

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.
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3. Solution
The value that makes the equation true.
The solution to the problem
x-3 = 7 is 10.
solution
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4. Inverse operations
Operations that “undo” each other.
The inverse operation of
addition is subtraction.
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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.
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6. Two-step equation
An equation that contains two different operations.
The equation 2x - 3 = 9 is a two-
step equation.
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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.
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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.
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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
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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.
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11. Equivalent Equations
Two equations that have the same solution.
The equations x + 10 = 20 and
X = 10 are equivalent
equations.
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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
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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.
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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.
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