Transcript Go for the gold

Lesson 3: Properties of equality
and solving equations
By the end of class you should be
able to:
• Apply the properties of equality to solve
single-step and multi-step linear equations
• Check a solution to a linear equation
Properties of equality
Addition Property
if a = b, then a + c = b + c
Subtraction Property if a = b, then a – c = b – c
Multiplication Property
if a = b, then ac = bc
Division Property
if a = b, then
Substitution Property
if a = b, then either a or b may be substituted
for the other in any equation (or inequality)
Properties of equality (cont’d)
Reflexive Property
a=a
Symmetric Property
if a = b, then b = a
Transitive Property
if a = b, and b = c, then a = c
Distributive Property
a(b + c) = ab + ac
What does it mean to find the
solution to an equation?
Determine the value for x such that when
substituted back into the original equation,
the resulting sentence is true.
Solving equations
• Solve:
x + 6= -2
Solving equations (cont’d)
How to check a solution
• Substitute the solution candidate into the
original equation
• Simplify both sides of the equal sign separately
(do not pass terms across the equal sign)
• Compare the end result of each side for
equality.