8A F11 Q7

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) How do we solve absolute value equations?
Answer:
1) We isolate everything inside of the absolute value signs.
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = \frac{11}{3}} . The second leads to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = -1}

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