LINEAR EQUATIONS
Algebra
Step 3.
Check the root.
2(-3) + 9 = -6 + 9 = 3
3[(-3) + 4] = 3(1) = 3
The root checks.
These same steps can be used to solve equations that include several unknowns. The result is
an expression for one of the unknowns in terms of the other unknowns. This is particularly
important in solving practical problems. Often the known relationship among several physical
quantities must be rearranged in order to solve for the unknown quantity. The steps are
performed so that the unknown quantity is isolated on the left-hand side of the equation.
Example 1:
Solve the equation ax - b = c for x in terms of a, b, and c.
Solution:
Step 1.
Using Axiom 1, add b to both sides of the equation.
ax - b + b
= c + b
ax
= c + b
Step 2.
Using Axiom 4, divide both sides of the equation by
a.
ax
a
c
b
a
x
c
b
a
Step 3.
Check the root.
ac
b
a
b
c
b
b
c
The root checks.
MA-02
Page 8
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