Difference between revisions of "004 Sample Final A, Problem 3"
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! Foundations | ! Foundations | ||
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| − | | | + | |1) What is the solution to <math>|x|\geq 3</math>? |
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| + | |2) How do you write <math>x\geq 2</math> in interval notation? | ||
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|Answer: | |Answer: | ||
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| − | | | + | |1) The solution is <math>x\geq 3</math> or <math>x\leq -3</math>. |
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| + | |2) <math>[2,\infty)</math> | ||
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! Step 1: | ! Step 1: | ||
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| − | | | + | |The inequality above means <math>4x+7\geq 5</math> or <math> 4x+7\leq -5</math>. |
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! Step 2: | ! Step 2: | ||
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| − | | | + | |Subtracting 7 from both sides of the inequalities, we get <math>4x\geq -2</math> or <math>4x\leq -12</math>. |
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! Step 3: | ! Step 3: | ||
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| − | | | + | |Dividing both sides of the inequalities by 4, we have <math>x\geq -\frac{1}{2}</math> or <math>x\leq -3</math>. |
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! Step 4: | ! Step 4: | ||
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| − | | | + | |Using interval notation, the solution is <math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math>. |
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! Final Answer: | ! Final Answer: | ||
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| − | | | + | |<math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math> |
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']] | [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 15:27, 4 May 2015
Solve. Provide your solution in interval notation.
| Foundations |
|---|
| 1) What is the solution 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|\geq 3} ? |
| 2) How do you write 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\geq 2} in interval notation? |
| Answer: |
| 1) The solution is 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\geq 3} or 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\leq -3} . |
| 2) 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,\infty)} |
Solution:
| Step 1: |
|---|
| The inequality above means 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 4x+7\geq 5} or 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 4x+7\leq -5} . |
| Step 2: |
|---|
| Subtracting 7 from both sides of the inequalities, we get 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 4x\geq -2} or 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 4x\leq -12} . |
| Step 3: |
|---|
| Dividing both sides of the inequalities by 4, we have 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\geq -\frac{1}{2}} or 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\leq -3} . |
| Step 4: |
|---|
| Using interval notation, the solution is 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 (-\infty,-3]\cup [-\frac{1}{2},\infty)} . |
| 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 (-\infty,-3]\cup [-\frac{1}{2},\infty)} |