Week 2.docx - If your assigned number Your “and” compound inequality Your “or” compound inequality is is is 29 –16 ≤ 2 9x ≤ 11 12 – x >

Week 2.docx - If your assigned number Your “and”...

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If your assigned number is: Your “and” compound inequality is : Your “or” compound inequality is : 29 –16 ≤ 2 + 9x ≤ 11 12 – x > 15 or 4x – 13 > 7 Problem #1 -16 ≤ 2 + 9x ≤ 11the compound inequalities means my answer should be greater than or equal to two and greater than or equal to eleven. For the negative sixteen you would first switch sides then, subtract by two then, divide by nine on both sides. My answer is below the working of the problem. -16 ≤ 2 + 9x ≤ 11 -16 ≤ 2 + 9x : x ≥ -2 2+9x ≥ -16 Switch sides 2 + 9x – 2 ≥ -16 - 2 Subtract 2 from both sides 9x ≥ -18 Simplify both sides (9x)/9 ≥ (-18)/9 Divide both side by 9 X = (9x)/9 or x = 1 Simplify and Divide first side (-18)/9 = -2 Simplify and Divide second side X ≥ -2 Answer Other side 2+9x ≤ 11 2 + 9x – 2 ≤ 11 – 2 Subtract 2 from both side 9x ≤ 9
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Unformatted text preview: Simplify 9x/9 ≤ 9/9 Divide both sides by 9 x ≤ 1 Answer x ≥ -2 and x ≤ 1 Combine the intervals The compounded inequalities are as follows:-2 ≤ x ≤ 1 written algebraically. Interval Notation of the union or intersection [-2, 1] the blue line represents the range of the compounded inequalities and the dots on the line graph are the start and stop points. Problem #2 12 – x > 15 or 4x – 13 > 7 12-x-12>15-12 Subtract 12 from both sides-x>3 Simplify (-x)(-1)<(3)(-1) Multiply both sides by -1to reverse the inequality X<-3 Simplify 4x-13>7 Second part 4x-13+13>7+13 Add 13 to both sides 4x>20 Simplify 4x÷4>20÷4 Divide both side by 4 x>5 Simplify x<-3 or x>5 Combine interval (-∞, -3] ∪ [5, ∞) Interval notation, note that these line do not intersect. Number Line x<-3 or x>5...
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