Term
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Definition
A statement that two algebraic expressions are equal.
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Term
| Addition Property of Equality |
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Definition
We can add the same number to each side of the equation without changing the solution.
x - 5 = 2
x - 5 + 5 = 2 + 5
x = 7 |
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Term
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Definition
Is addition of the opposite.
x + 4 = 10
x + 4 - 4 = 10 - 4
x = 6 |
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Term
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Definition
Is not the final line of the equation, that is just the check. The solution is the value equal to x.
x + 5 = 2
x + 5 - 5 = 2 - 5
x = -3 |
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Term
| Multiplication Property of Equality |
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Definition
If the coefficient of x on the left side is 3, not 1 as desired, we need to get to the point where it is 1.
3x = 15
1/3(3x) = 1/3 (15)
(1/3 x 3)x = 1/3 (15)
1x = 5
x = 5 |
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Term
| When using the addition property of equality, you can subtract the same number from each side of the equation. The mulitplication property of equality allows dividing each side of the equation by the same nonzero number. |
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Definition
3x = 15
3x/3 = 15/3
x = 5
***Do not divide each side by the variable, since the variable might be equal to 0.*** |
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Term
| It is usually easier to multiply on each side if the coefficient of the variable is a fraction, and divide on each side if the coefficient is an integer or a decimal! |
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Definition
Example
-3/4x = 12
It's easier to multiply by -4/3, the reciprocal of -3/4, than to divide by -3/4. On the other hand, to solve -5x = -20, it's easier to divide by -5 than to multiply by -1/5. |
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