The equation is .
Apply division property of equality: Divide each side by 4.
\Combine like terms using distributive property: ab + ac = a(b + c).
\ (Cancel common terms)
Write two cases:
\Case-1:
Case-2:
Solve the equation for Case-1.
\Apply subtraction property of equality: Subtract x from each side.
\Apply commutative property of addition: .
(Apply Additive inverse property:
)
(ApplyAdditive identity property: 2 + 0 = 2)
(Subtract:
)
Apply subtraction property of equality: Subtract 4 from each side.
\ (Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Subtract:
)
Apply division property of equality: Divide each side by 2.
\ (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.
\Solve the equation for Case-2.
\ (Product of two different signs is neative)
Apply subtraction property of equality: Subtract 3x from each side.
\Apply commutative property of addition: .
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Subtract:
)
Apply addition property of equality: Add 2 to each side.
\ (Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Add:
)
Apply division property of equality: Divide each side by negative 4.
\
(Cancel common terms)
(Divide:
)
Check:
\To check the solution, substitute in original equation.
(Multiply:
)
(Add:
)
(Add:
)
(The absolute value of
is
)
Compare the values the equation is true.
The solution set is .