Difference between revisions of "008A Sample Final A, Question 7"
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| − | !Foundations | + | !Foundations: |
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|1) How do we get to the first key step in solving any function involving absolute value equations? | |1) How do we get to the first key step in solving any function involving absolute value equations? | ||
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| − | ! Step 1: | + | ! Step 1: |
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|Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2. | |Isolate the absolute values. First by adding 7 to both sides, then dividing both sides by 2. | ||
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|Now we create two equations: <math>3x - 4 = 7</math> and <math>3x - 4 = -7</math>. | |Now we create two equations: <math>3x - 4 = 7</math> and <math>3x - 4 = -7</math>. | ||
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| − | ! Step 3: | + | ! Step 3: |
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|Now we solve both equations. The first leads to the solution <math>x = \frac{11}{3}</math>. The second leads to <math>x = -1</math> | |Now we solve both equations. The first leads to the solution <math>x = \frac{11}{3}</math>. The second leads to <math>x = -1</math> | ||
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| − | ! Final | + | ! Final Answer: |
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|<math>x = \frac{11}{3}, -1</math> | |<math>x = \frac{11}{3}, -1</math> | ||
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[[008A Sample Final A|<u>'''Return to Sample Exam</u>''']] | [[008A Sample Final A|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 22:53, 25 May 2015
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: |
|---|
| 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 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} . |
| 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 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.} |
| Step 2: |
|---|
| 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} . |
| 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} |
| Final Answer: |
|---|
| 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} |