Question: Solve 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 2\vert 3x-4\vert -7 = 7}
| Foundations
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| 1) How do we get to the first key step in solving any function involving absolute value equations?
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| 2) How do we solve absolute value equations?
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| Answer:
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| 1) We isolate everything inside of the absolute value signs.
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| 2) We create two equations based on whether the expression inside the absolute value is positive or negative.
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| Then we solve both equations.
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Solution:
| Step 1:
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| Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2.
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| This 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 \vert 3x - 4\vert = 7.}
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| Step 2:
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| Now we create two equations: 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 3x - 4 = 7}
and 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 3x - 4 = -7}
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| Step 3:
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| 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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| Final Solution:
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| 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}, -1}
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