Answer:
x+8=10
x−4=22
x÷3=6
7x=28
Step-by-step explanation:
George has cut down a 60ft high oak tree. He now wants to chop it into smaller pieces. He first cuts it into two pieces that are both 30ft. And then he continues on into making ten pieces that all are 6ft long before loading them onto his truck.
picture08
By looking at the different pieces of wood we can see that the following holds true.
60=30+30=6+6+6+6+6+6+6+6+6+6
This is called the reflexive property of equality and tells us that any quantity is equal to itself
a=a
We can also use this example with the pieces of wood to explain the symmetric property of equality. This property states that if quantity a equals quantity b, then b equals a.
ifa=b,thenb=a
Or if we use our example
if60=30+30,then30+30=60
Another property that can be explained by this is the transitive property of equality. It tells us that if a quantity a equals quantity b, and b equals the quantity, c, then a and c are equal as well.
ifa=bandb=c,thena=c
Or in the numbers taken from the oak tree example
if60=30+30
and30+30=6+6+6+6+6+6+6+6+6+6
then60=6+6+6+6+6+6+6+6+6+6
Since we know that 30 + 30 = 20 + 40 and that 30 + 30 = 60 we can substitute 30 + 30 for 20 + 40 and get 60 = 20 + 40. This is called the substitution property of equality.
If a = b, then a can be substituted for b in any expression.George has cut down a 60ft high oak tree. He now wants to chop it into smaller pieces. He first cuts it into two pieces that are both 30ft. And then he continues on into making ten pieces that all are 6ft long before loading them onto his truck.
picture08
By looking at the different pieces of wood we can see that the following holds true.
60=30+30=6+6+6+6+6+6+6+6+6+6
This is called the reflexive property of equality and tells us that any quantity is equal to itself
a=a
We can also use this example with the pieces of wood to explain the symmetric property of equality. This property states that if quantity a equals quantity b, then b equals a.
ifa=b,thenb=a
Or if we use our example
if60=30+30,then30+30=60
Another property that can be explained by this is the transitive property of equality. It tells us that if a quantity a equals quantity b, and b equals the quantity, c, then a and c are equal as well.
ifa=bandb=c,thena=c
Or in the numbers taken from the oak tree example
if60=30+30
and30+30=6+6+6+6+6+6+6+6+6+6
then60=6+6+6+6+6+6+6+6+6+6
Since we know that 30 + 30 = 20 + 40 and that 30 + 30 = 60 we can substitute 30 + 30 for 20 + 40 and get 60 = 20 + 40. This is called the substitution property of equality.
If a = b, then a can be substituted for b in any expression.
