Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
526<br />
<strong>Chapter</strong> 9 Solving Equations and Inequalities<br />
9. Solve: 5(3a 2 4) 2 14a 5 25<br />
Example 9<br />
Solve: 4(2a 2 3) 2 7a 5 2 2 5.<br />
Solution We must begin by applying the distributive property to separate<br />
terms on the left side of the equation. Following that, we combine similar terms<br />
and then apply the addition property of equality.<br />
4(2a 2 3) 2 7a 5 2 2 5 Original equation<br />
8a 2 12 2 7a 5 2 2 5 Distributive property<br />
a 2 12 5 23 Simplify each side<br />
a 2 12 1 12 5 23 1 12 Add 12 to each side<br />
a 5 9<br />
Addition<br />
A Note on Subtraction<br />
Although the addition property of equality is stated for addition only, we can subtract<br />
the same number from both sides of an equation as well. Because subtraction<br />
is defined as addition of the opposite, subtracting the same quantity from<br />
both sides of an equation will not change the solution. If we were to solve the<br />
equation in Example 3 using subtraction instead of addition, the steps would look<br />
like this:<br />
x 1 4 5 22<br />
x 1 4 2 4 5 22 2 4<br />
x 5 26<br />
Original equation<br />
Subtract 4 from each side<br />
Subtraction<br />
In my experience teaching algebra, I find that students make fewer mistakes if<br />
they think in terms of addition rather than subtraction. So, you are probably better<br />
off if you continue to use the addition property just the way we have used it in<br />
the examples in this section. But, if you are curious as to whether you can subtract<br />
the same number from both sides of an equation, the answer is yes.<br />
Getting Ready for Class<br />
After reading through the preceding section, respond in your own<br />
words and in complete sentences. An answer of true or false should<br />
be accompanied by a sentence explaining why the answer is true or<br />
false.<br />
1. What is a solution to an equation?<br />
2. True or false? According to the addition property of equality, adding the<br />
same value to both sides of an equation will never change the solution<br />
to the equation.<br />
3. Show that x 5 5 is a solution to the equation 3x 1 2 5 17 without solving<br />
the equation.<br />
4. True or false? The equations below have the same solution.<br />
Equation 1: 7x 1 5 5 19<br />
Equation 2: 7x 1 5 1 3 5 19 1 3<br />
Answer<br />
9. 45
Change language