008A Sample Final A, Question 7

Question: Solve $2\vert 3x-4\vert -7=7$

Foundations:
1) How do we get to the first key step in solving any function involving absolute value equations?
2) After this first key step how do we finish solving absolute value equations?
Answer:
1) We isolate the absolute value sign, so in this case we isolate $\vert 3x-4\vert$.
2) We create two equations based on whether the expression inside the absolute value is positive or negative.
Then we solve both equations.

Solution:

Step 1:
Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2.
This leads to $\vert 3x-4\vert =7.$

Step 2:
Now we create two equations: $3x-4=7$ and $3x-4=-7$.

Step 3:
Now we solve both equations. The first leads to the solution $x={\frac {11}{3}}$. The second leads to $x=-1$

Final Solution:
$x={\frac {11}{3}},-1$

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