Page 180 - ArithBook5thEd ~ BCC

Solution. When we substitute −4for y in the equation, we get

−3(−4) = 12
12 = 12, a true statement.

Example 226. Show that 10 is not asolution to the equation z − 9= −1.

Solution. When we substitute 10 for z in the equation, we get

10 − 9= −1
−1= 1, a false statement.

2
Example 227. Show that 3 is a solution to the equation 2 − t =0, but 4 is not.
3
Solution. When we substitute 3 for t,we obtain

2 3 ✁✕
✁
2 − · =0
✁ 3 ✁✕ 1
2 − 2= 0
0= 0, a true statement.

When we substitute 4 for t,we obtain

2 4
2 − · =0
3 1
8
2 − =0,
3
2
− =0, a false statement.
3

Here is the formal definition of the subject of this section.

Alinear equation in one variable x is an equation that can
be written in the form

ax + b = c
for some numbers a, b and c,with a ̸=0.

Such an equation always has a unique (i.e., exactly one) solution.

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