Chapter 9 - XYZ Custom Plus

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Chapter 9 Solving Equations and Inequalities
8. Solve for x:
25 1 4 5 2x 2 11 1 3x
Example 8
Solve for x: 28 1 11 5 4x 2 11 1 3x
Solution
We begin by simplifying each side separately.
28 1 11 5 4x 2 11 1 3x
3 5 7x 2 11 Simplify both sides
3 1 11 5 7x 2 11 1 11 Add 11 to both sides
14 5 7x Addition
14
} 5 } 7x
Divide both sides by 7
7 7
2 5 x or x 5 2
Again, it makes no difference which side of the equation x ends up on, so long as
it is just one x.
COMMON MISTAKES
Before we end this section, we should mention a very common mistake
made by students when they first begin to solve equations. It involves trying
to subtract away the number in front of the variable—like this:
7x 5 21
7x 2 7 5 21 2 7 Add 27 to both sides
x 5 14 m88888 Mistake
The mistake is not in trying to subtract 7 from both sides of the equation.
The mistake occurs when we say 7x 2 7 5 x. It just isn’t true. We can add
and subtract only similar terms. The terms 7x and 7 are not similar, because
one contains x and the other doesn’t. The correct way to do the problem is
like this:
7x 5 21
} 7 x
} 5 } 2 1
} Divide both sides by 7
7 7
x 5 3
Division
Getting Ready for Class
After reading through the preceding section, respond in your own
words and in complete sentences.
1. True or false? Multiplying both sides of an equation by the same nonzero
quantity will never change the solution to the equation.
2. If we were to multiply the right side of an equation by 2, then the left
side should be multiplied by .
3. Dividing both sides of the equation 4x 5 220 by 4 is the same as multiplying
both sides by what number?
Answer
8. 2