Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
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524<br />
<strong>Chapter</strong> 9 Solving Equations and Inequalities<br />
2. Is a 5 23 the solution to the<br />
equation 6a 2 3 5 2a 1 4?<br />
ExAmplE 2<br />
Is a 5 22 the solution to the equation 7a 1 4 5 3a 2 2?<br />
SOlutiOn When a 5 22<br />
the equation 7a 1 4 5 3a 2 2<br />
becomes 7(22) 1 4 5 3(22) 2 2<br />
214 1 4 5 26 2 2<br />
210 5 28 A false statement<br />
Because the result is a false statement, we must conclude that a 5 22 is not<br />
the<br />
solution to the equation 7a 1 4 5 3a 2 2.<br />
b Addition Property of Equality<br />
We want to develop a process for solving equations with one variable. The most<br />
important property needed for solving the equations in this section is called the<br />
addition property of equality. The formal definition looks like this:<br />
Addition property of Equality<br />
Let A, B, and C<br />
represent algebraic expressions.<br />
If<br />
then<br />
A 5 B<br />
A 1 C 5 B 1 C<br />
In words: Adding the same quantity to both sides of an equation never changes<br />
the solution to the equation.<br />
This property is extremely useful in solving equations. Our goal in solving equations<br />
is to isolate the variable on one side of the equation. We want to end up<br />
with an equation of the form<br />
x 5 a number<br />
To do so we use the addition property of equality. Remember to follow this basic<br />
rule of algebra: Whatever is done to one side of an equation must be done to the<br />
other side in order to preserve the equality.<br />
3. Solve for x: x 1 5 5 22<br />
Note<br />
With some of the equations<br />
in this section,<br />
you will be able to see<br />
the solution just by looking at<br />
the equation. But it is important<br />
that you show all the steps used<br />
to solve the equations anyway.<br />
The equations you come across in<br />
the future will not be as easy to<br />
solve, so you should learn the steps<br />
involved very well.<br />
ExAmplE 3<br />
Solve for x: x 1 4 5 22<br />
SOlutiOn<br />
We want to isolate x<br />
on one side of the equation. If we add 24 to<br />
both sides, the left side will be x 1 4 1 (24), which is x 1 0 or just x.<br />
x 1 4 5 22<br />
x 1 4 1 (−4) 5 22 1 (−4)<br />
x 1 0 5 26<br />
x 5 26<br />
Add 24 to both sides<br />
Addition<br />
x + 0 = x<br />
The solution is 26. We can check it if we want to by replacing x<br />
with 26 in the<br />
original equation:<br />
When x 5 26<br />
the equation x 1 4 5 22<br />
becomes 26 1 4 5 22<br />
22 5 22 A true statement<br />
Answers<br />
2. No 3. 27
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