Solving Equations with Negative Numbers

Solving Equations With Negative Numbers

The same methods used for other equations apply to equations that involve negative numbers. We use the properties of equality to isolate the variable (usually x) on one side of the equal sign.

Example: Algebraically solve x – 6 = -2

Add 6 to both sides to get

x – 6 + 6 = -2 + 6 which simplifies to

x + 0 = 4 which simplifies to x = 4

In this example we used the Addition Property of Equality, which states that you may add equal amounts to both sides of an equation without changing the equation.

Also, we used the Addition Property of Zero, which assures us that x + 0 simplifies to x.

Example: Algebraically solve x + (-4) = -12

Add 4 to both sides to get

x + (-4) + 4 = -12 + 4 which simplifies to

x + 0 = -8 which simplifies to x = -8

In this example we again used the Addition Property of Equality and the Addition Property of Zero.

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Example: Algebraically solve -3x = -12

Divide both sides by -3 to get

-3x = -12

-3 -3 which simplifies to

1x = 4 which simplifies to x = 4

In this example we again used the Division Property of Equality and the Multiplication Property of One.

Also note that –12 over –3, as a fraction, is the same as –12 divided by –3, which results in the positive answer of 4.

Example: Algebraically solve -20x + 1 = -2

Add –1 to both sides to get

-20x + 1 + (-1) = -2 + (-1) which simplifies to

-20x + 0 = -3 which simplifies to

-20x = -3

Divide both sides by -20 to get

-20x = - 3

-20 -20 which simplifies to

1x = 3/20 which simplifies to x = 3/20

In this example we used the Addition Property of Equality, the Addition Property of Zero and the Multiplication Property of One. Note that the fraction –3/(-20) represents the division of two numbers. Since both numbers are negative, the fraction becomes positive.