The equation is .
According to division property of equality: if , then
.
(Divide each side by 3)
(Cancel common terms)
Write two cases:
\Case-1: a = b
\Case-2: a = b
Solve the equation for Case-2.
\According to Multiplication property of equality: if , then
.
(Multiply each side by 3)
(Cancel common terms)
(Apply Distributive property: a(b - c) = ab - ac)
(Multiply:
)
According to addition property of equality: if a = b, then a + c = b + c.
\ (Add 15 to each side)
(Apply Additive inverse property:
)
(Subtract 2p from each side)
(Apply Comutative property: a + b = b + a)
(Apply Additive inverse property:
)
(Subtract:
)
Check:
\To check the solution, substitute in original equation.
(Subtract:
)
(Absolute value: |10| = 10)
30 = 30 (Multiply: )
Compare the values the equation is true. is a solution.
Solve the equation for Case-2.
\According to Multiplication property of equality: if , then
.
(Multiply each side by 3)
(Cancel common terms)
(Apply Distributive property: a(b - c) = ab - ac)
(Multiply:
)
According to addition property of equality: if a = b, then a + c = b + c.
\ (Add 15 to each side)
(Apply Additive inverse property:
)
(Add 2p to each side)
(Apply Comutative property: a + b = b + a)
(Apply Additive inverse property:
)
(Add:
)
According to division property of equality: if , then
.
(Divide each side by 5)
(Cancel common terms)
(Divide:
)
Check:
\To check the solution, substitute in original equation.
(Subtract :
)
(Absolute value: |
2| = 2)
6 = 6 (Multiply: )
Compare the values the equation is true. is a solution.
The solutions are 15 and 3. The solution set is .