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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 50 Page 33

The solutions of the absolute value equations can sometimes be extraneous.

Error: Solutions not checked.
Correct Solution: No solutions.

Practice makes perfect

Looking at the provided work, no errors have been committed. The absolute value equation was written as two equations correctly, and inverse operations were applied correctly. However, the solutions were not checked. When solving absolute value equations, we have to check if the solutions are not extraneous.

Checking x=-2

Let's check if x=-2 satisfies the original equation.

|5x+8|=x

x= - 2

|5({\color{#0000FF}{\text{-} 2}})+8|\stackrel{?}={\color{#0000FF}{\text{-} 2}}

a(- b)=- a * b

|\text{-} 5\cdot 2+8|\stackrel{?}=\text{-} 2

Multiply

|\text{-} 10 +8|\stackrel{?}=\text{-} 2

Add terms

|\text{-} 2 | \stackrel{?}= \text{-} 2

|-2|=2

2 ≠ - 2

We ended with a false statement, so x=- 2 is an extraneous solution.

Checking x=-4/3

Now let's substitute x=- 43 into the equation.

|5x+8|=x

x= -4/3

\left|5\left({\color{#009600}{\text{-}\dfrac{4}{3}}}\right)+8\right|\stackrel{?}={\color{#009600}{\text{-}\dfrac{4}{3}}}

a(- b)=- a * b

\left|\text{-} 5\cdot \dfrac{4}{3}+8\right|\stackrel{?}=\text{-}\dfrac{4}{3}

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a*b/c= a* b/c

\left|\text{-}\dfrac{20}{3} +8\right|\stackrel{?}=\text{-}\dfrac{4}{3}

Write as a fraction

\left|\text{-}\dfrac{20}{3} +\dfrac{24}{3}\right|\stackrel{?}=\text{-}\dfrac{4}{3}

Add terms

\left|\text{-}\dfrac{4}{3} \right| \stackrel{?}= \text{-}\dfrac{4}{3}

|-4/3|=4/3

4/3 ≠ -4/3

We ended up with another false statement, so x=- 43 is also an extraneous solution.

Subchapter links

Communicate Your Answer p.27

Monitoring Progress p.28-31

Exercises p.32-34