Answer/Discussion
to 1a
Using the definition of absolute value there will be two equations that
we will need to set up to get rid of the absolute value, because there
are two places on the number line that are 10 units away from zero: 10
and -10.
*Inv. of add. 2 is sub. 2
*Inv. of mult. by 7 is div. by 7
*Inv. of add. 2 is sub. 2
*Inv. of mult. by 7 is div. by 7
If you would have only come up with an answer of x = 8/7, you would not have gotten all solutions to this problem.
Again, it is important to note that we are using the definition of absolute value to set the two equations up. Once you apply the definition and set it up without the absolute value, you just solve the linear equation as shown in Tutorial 14: Linear Equations in One Variable.
There are two solutions to this absolute value equation: 8/7
and -12/7.
Answer/Discussion
to 1b
Answer: No solution.
Answer/Discussion
to 1c
Using the definition of absolute value, there will be two equations
that we will need to set up to get rid of the absolute value because there
are two places on the number line that are 8 units away from zero: 8 and
-8.
*Quad. eq. in standard form
*Factor
the trinomial
*Use Zero-Product
Principle
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
*Quad. eq. in standard form
*Factor
the trinomial
*Use Zero-Product
Principle
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
If you would have only come up with an answer of x = 6 and -4, you would not have gotten all solutions to this problem.
Again, it is important to note that we are using the definition of absolute value to set the two equations up. Once you apply the definition and set it up without the absolute value, you just solve the quadratic equation as shown in Tutorial 17: Quadratic Equations.
There are four solutions to this absolute value equation: 6, -4,
4, and -2.
Last revised on Dec. 16, 2009 by Kim Seward.
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