3.4-1
See this example:
Solve each equation by hand.
a.
= 11
b.
= 21
c.
3
–3=
12
Solution
a. If x represents an algebraic expression and a > 0, then
x = a or x = a.
The solutions of
= a will have two solutions:
= 11 are given by
2x – 3 = 11
2x = 14
x=7
or
2x – 3 =
2x = 8
x= 4
11
Optional:
Substituting these values into the original equation verifies the solutions:
= 11
= 11
= 11
True
and
= 11
= 11
= 11
True
b. Since the absolute value of a quantity is never negative, the equation
solution.
=
21 has no
c. To solve the equation algebraically, begin by isolating the absolute value expression.
3
– 3 = 12
3
= 9
=3
Next, the solutions of
2x – 5 = 3
x=4
or
= 3 are given by
2x – 5 =
x=1
3