The equation is .
According to division property of equality: if , then
.
(Divide each side by 7)
(Cancel common terms)
(Divide:
)
Write two cases:
\Case-1: a = b
\Case-2: a = b
Solve the equation for Case-2.
\According to addition property of equality: if a = b, then a + c = b + c.
\ (Add 13 to each side)
(Apply Additive inverse property:
)
(Add: 5 + 13 = 18)
(Divide each side by 4)
(Cancel common terms)
Check:
\To check the solution, substitute in original equation.
(Cancel common terms)
(Subtract:
)
(Absolute value: |5| = 5)
35 = 35 (Multiply: )
Compare the values the equation is true. is a solution.
Solve the equation for Case-2.
\According to addition property of equality: if a = b, then a + c = b + c.
\ (Add 13 to each side)
(Apply Additive inverse property:
)
(Add: -5 + 13 = 8)
(Divide each side by 4)
(Cancel common terms)
(Divide:
)
Check:
\To check the solution, substitute in original equation.
(Multiply:
)
(Subtract:
)
(Absolute value: |
5| = 5)
35 = 35 (Multiply: )
Compare the values the equation is true. is a solution.
The solutions are and 2. The solution set is
.