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

Latest revision as of 15:27, 4 May 2015

Solve. Provide your solution in interval notation. $\vert 4x+7\vert \geq 5$

Foundations
1) What is the solution to $\|x\|\geq 3$ ?
2) How do you write $x\geq 2$ in interval notation?
Answer:
1) The solution is $x\geq 3$ or $x\leq -3$ .
2) $[2,\infty )$

Solution:

Step 1:
The inequality above means $4x+7\geq 5$ or $4x+7\leq -5$ .

Step 2:
Subtracting 7 from both sides of the inequalities, we get $4x\geq -2$ or $4x\leq -12$ .

Step 3:
Dividing both sides of the inequalities by 4, we have $x\geq -{\frac {1}{2}}$ or $x\leq -3$ .

Step 4:
Using interval notation, the solution is $(-\infty ,-3]\cup [-{\frac {1}{2}},\infty )$ .

Final Answer:
$(-\infty ,-3]\cup [-{\frac {1}{2}},\infty )$

@@ Line 3: / Line 3: @@
 ! Foundations
 |-
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+|1) What is the solution to <math>|x|\geq 3</math>?
+|-
+|2) How do you write <math>x\geq 2</math> in interval notation?
 |-
 |Answer:
 |-
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+|1) The solution is <math>x\geq 3</math> or <math>x\leq -3</math>.
+|-
+|2) <math>[2,\infty)</math>
 |}
@@ Line 16: / Line 20: @@
 ! Step 1:
 |-
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+|The inequality above means <math>4x+7\geq 5</math> or <math> 4x+7\leq -5</math>.
-|-
-|
 |}
@@ Line 24: / Line 26: @@
 ! 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>.
 |}
@@ Line 30: / Line 32: @@
 ! 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>.
-|-
-|
-|-
-|
-|-
-|
 |}
@@ Line 42: / Line 38: @@
 ! Step 4:
 |-
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+|Using interval notation, the solution is <math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math>.
-|-
-|
-|-
-|
 |}
@@ Line 52: / Line 44: @@
 ! Final Answer:
 |-
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+|<math>(-\infty,-3]\cup [-\frac{1}{2},\infty)</math>
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]