Math 116

When we use the rundown principle, we sometimes say that we add the corresponding repress on both sides of the equation. This is also true for subtraction, since we stick out express every subtraction as an gain. That is, since is equivalent to the auxiliary principle tells us that we can subtract the same number on both sides of the equation. EXAMPLE 6 do work: We have Using the step-up principle: adding 5 on both sides or subtracting 5 on both sides Simplifying personal identity property of 0 To check the answer, we substitute 12 in the original equation. Check: TRUE The solution of the original equation is 12. In Example 6, to get x alone, we used the addition principle and subtracted 5 on both sides. This eliminated the 5 on the left. We started with and, using the addition principle, we found a simpler equation for which it was easy to guess the solution. The equations and are equivalent. Do Exercise 9.

Now we use the addition principle to solve an equation that involves a subtraction. EXAMPLE 7 Solve: We have Using the addition principle: adding 4 on both sides Simplifying Identity property of 0 Check: TRUE The solution is 14. Do Exercise 10. 10 14  4 ? 10 a  4
10 a
14. a
0
14 a  4
4
10
4 a  4
10 a  4
10. x
12 x
12 x
5
7 x
5
7, 7 12
5 ? 7 x
5
7 x
12. x
0
12 x
5  5
7  5 x
5
7 x
5
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