The equation is
Division property of equality:
\For any real numbers a, b and c, with , if
then
(Divide each side by 4)
(Distribute 4)
(Cancel common terms)
Write two cases:
\Case-1: .
Case-2:
\
Combine like terms using distributive property: .
Solve the equation for Case-1.
\
(Subtract 3x from each side)
(Apply Commutative property:
.)
(Apply Additive inverse property:
)
(ApplyAdditive identity property:
)
(Subtract:
)
(Subtract 2 from each side)
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Subtract:
)
(Divide each side by -2)
(Cancel common terms)
Check:
\To check the solution, substitute in original equation.
(Multiply:
)
(Add:
)
(The absolute value of 1 is 1.)
Compare the values the equation is true.
(Product of two opposite signs is neative)
(Subtract 3x from each side)
(Apply Commutative property;
.)
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Subtract:
)
(Add 2 to each side)
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Add:
)
(Divide each side by4)
(Cancel common terms)
(Divide:
)
Check:
\To check the solution, substitute in original equation.
(Multiply:
)
(Add:
)
(The absolute value of
is
.)
Compare the values the equation is true.
The solution set is
\