Linear Equation Flashcards
a mathematical statement that tells you that two quantities are equal in value.
Equation
Example:Which of the following are equations?
a. 2x + 3 = – 9
b. x = – 7
c. x – 5
Solution:The mathematical statements inaandbare equations because they have an equal sign. On the other hand,cis not an equation because of the absence of an equal sign
quantities on the left of the equal sign.
The left-hand side of the equation
quantities on the right of the equal sign.
The right-hand side of the equation
Example:Is x = 5 the solution to x + 2 = 7?
Solution:Yes, because if we substitute x = 5 to x + 2 = 7:
x + 2 = 7
(5) + 2 = 7
7 = 7
The left-hand side and the right-hand side of the equation are equal. Indeed, x = 5 is the solution to x + 2 = 7.
rules or principles that allow us to manipulate equations so we can determine the values of the unknown variable.
properties of equality
This property is pretty obvious and logical. The value of a number is always equal to itself.
For instance, 1020 will always be equal to 1020. If someone tells you that 1020 = 1100, he is logically false since 1020 is always equal to 1020
Reflexive Property of Equality
This property tells us that in an equation if we switch the positions of the quantities on the left-hand side and the right-hand side of the equation, the equation will still hold. This also implies that both sides of the equation are of the same value.
Symmetric Property of Equality
tells us that if a quantity is equal to a second quantity, and if the second quantity is equal to a third quantity, then we can conclude that the first quantity is equal to the third quantity.
Transitive Property of Equality
For any real numbers p, q, and r:
If p = q and q = r, then p = r
tells us that if we add a certain number to two equal quantities, the result will still be equal.
Addition Property of Equality (APE)
tells us that if we subtract two equal quantities by the same number, the results will still be equal.
Subtraction Property of Equality (SPE)
tells us that the results will still be equal if we multiply two equal quantities by the same number.
For example, we know that 2 + 2 = 3 + 1. Suppose that we multiply both sides of this equation by 5:
As shown above, the results will still be equal even after multiplying both sides by the same number.
Multiplication Property of Equality
This property tells us that the results will still be equal if we divide two equal quantities by the same number (that number can be any number but must not be equal to 0).
Division Property of Equality
This property tells us that multiplying the sum of two or more addends is equal to the result when we multiply the addends by that number and add them.
Distributive Property of Equality
If x = y, then either x or y can be substituted into any equation for the other.
Substitution Property of Equality
p = p
Reflexive Property
If p = q, then q = p
Symmetric Property
If p = q and q = r, then p = r
Transitive Property
If p = q, then p + r = q + r
Addition Property of Equality
If p = q, then p – r = q – r
Subtraction Property of Equality
If p = q, then pr = qr
Multiplication Property of Equality
If p = q, then p/r = q/r where r0
Division Property of Equality