Solving Equations

Vocabulary words

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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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Solution

The value that makes the equation true.

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

solution

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Inverse operations

Operations that “undo” each other.

The inverse operation of addition is subtraction.

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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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Two-step equation

An equation that contains two different operations.

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

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Terms

The coefficients, variables and constants that make up an equation.

In the expression3x + 4y + 7 - 12 + 10x + 6y…3x, 4y, 7, -12, 10x, 6y are all terms.

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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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Coefficient

The number in front of a variable.

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

= 3b b b

coefficient

b

variable

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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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Equivalent Equations

Two equations that have the same solution.

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

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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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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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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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