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