Difference between revisions of "004 Sample Final A, Problem 3"

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(Created page with "<span class="exam"> Solve. Provide your solution in interval notation.     <math>\vert 4x + 7\vert \ge 5</math>")
 
 
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<span class="exam"> Solve. Provide your solution in interval notation. &nbsp;&nbsp;&nbsp;&nbsp;<math>\vert 4x + 7\vert \ge 5</math>
 
<span class="exam"> Solve. Provide your solution in interval notation. &nbsp;&nbsp;&nbsp;&nbsp;<math>\vert 4x + 7\vert \ge 5</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|-
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|1) What is the solution to <math>|x|\geq 3</math>?
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|-
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|2) How do you write <math>x\geq 2</math> in interval notation?
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|-
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|Answer:
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|-
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|1) The solution is <math>x\geq 3</math> or <math>x\leq -3</math>.
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|-
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|2) <math>[2,\infty)</math>
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|}
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Solution:
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{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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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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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 2:
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|-
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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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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 3:
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|-
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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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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 4:
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|-
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|Using interval notation, the solution is <math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Final Answer:
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|-
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|<math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math>
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|}
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[[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 ?
2) How do you write in interval notation?
Answer:
1) The solution is or .
2)


Solution:

Step 1:
The inequality above means or .
Step 2:
Subtracting 7 from both sides of the inequalities, we get or .
Step 3:
Dividing both sides of the inequalities by 4, we have or .
Step 4:
Using interval notation, the solution is .
Final Answer:

Return to Sample Exam

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