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2/9: 6.4 solving an absolute value function
due: february 10 at 8:15 am
grade: 0%
complete: 10%

1. absolute value function
2. absolute value graph
3. absolute value equation
4. absolute value single solution
5. absolute value equation
6. absolute value equation

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question

1. the graphs of the equations $y = 5$ and $y = 2|x - 4| - 3$ are shown. solve the equation

$5 = 2|x - 4| - 3$.
answer attempt 1 out of 2
⊕ additional solution ⊖ no solution
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Explanation:

Step1: Isolate absolute value term

Add 3 to both sides:
$5 + 3 = 2|x - 4|$
$8 = 2|x - 4|$
Divide by 2:
$\frac{8}{2} = |x - 4|$
$4 = |x - 4|$

Step2: Split into two equations

Absolute value rule: $|A|=B \implies A=B$ or $A=-B$:
$x - 4 = 4$ or $x - 4 = -4$

Step3: Solve for x in each case

For $x - 4 = 4$:
$x = 4 + 4$
$x = 8$

For $x - 4 = -4$:
$x = -4 + 4$
$x = 0$

Answer:

$x=0$ and $x=8$