1. Solving Inequalities > < < > > <
Set Builder Notation
{ x| x < –2.7; x  R }
created & designed by Tammy the Tutor © MathRoom Learning Service

2. ____________________
Instructions
INSTRUCTIONS
Solve for Real Number values of x : Show all your work. a) Write the solution as an interval. b) Draw a number line of the solution. Click your mouse to see the solution.
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3. Question 1 step 1: transpose terms to get – 4x < – 121.
step 1: transpose terms to get – 4x < – 12
step 2: divide both sides by – 4 x > 3
solution: ] 3, ∞ [

4. Question 2 2. step 1: transpose terms to get – 5x < 4
step 2: divide both sides by – 5 x > – 4/5
solution: ] – 4/5, ∞ [
–2 –

5. Question 3 step 1: multiply through by 12: – 10x < 9 + 32x3.
step 1: multiply through by 12: – 10x < x
step 2: collect like terms – 42x < 9
step 3: divide by – 42 x > – 9/42 or x > – 3/14 –
solution: [–3/14, ∞[

6. Question 4 step 1: remove brackets: 4x² – 8x < 4x² – 14x + 64.
step 1: remove brackets: 4x² – 8x < 4x² – 14x + 6
step 2: collect like terms to get: 6x < 6
step 3: divide both sides by 6 x < 1
solution: ] – ∞, 1 [
–2 –

7. Question 5 step 1: transpose, collect terms: 12x > – 55.
step 1: transpose, collect terms: 12x > – 5
step 2: divide both sides by 12 x > – 5/12
solution: [ –5/12, ∞ [
–2 –

8. Set Builder Notation 1-2 { x| x > 2.5; x  R }
Write Set Builder Notation for these: All sets are from the Real Numbers (R) Click your mouse to see the solution. 1.
{ x| x > 2.5; x  R } 2.
{ y| y < –7; y  R }

9. Set Builder Notation 3-4 step 1: transpose terms to get m³ – m² = – 53.
step 1: transpose terms to get m³ – m² = – 5
solution { m| m³ – m² = – 5; m  R } 4.
step 1: divide by 2 to get t² = 5
solution { t| t² = 5; t  R }

10. ____________________
Word Problem #1
Find all Natural Numbers such that 5 more than 3 times the number is greater than 4, but less than or equal to 27.
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11. Problem #1: Set-Up
We need Natural Numbers such that 5 more than 3 times the number is greater than 4, but less than or equal to 27.
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step 1: name the variable (make a “ let ” statement) let n = the number
step 2: translate words to a math statement: 4 < 3n + 5  27

12. Problem #1: Solution step 3: solve the inequation: 4 < 3n + 5  27
since n is a Natural Number, 0 < n  7
The numbers are 1, 2, 3, 4, 5, 6, or 7

13. Word Problem #2
x – 4
x – 2
The area of this rug is greater than 3 m² but less than or equal to 15 m².
a) Find integer values for x.
b) Find the exact area.
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14. Problem #2: Set-Up
x – 4
x – 2
a) Find integer values for x if the Area > 3 but  15. Area = (x – 4)(x – 2)
SOLUTION:
step 1: write the inequality:
3 < (x – 4)(x – 2)  15
step 2: simplify the inequality:
3 < x² – 6x + 8  15

15. Problem #2: Solution step 3: solve 2 separate quadratic inequalities
0 < x² – 6x x² – 6x – 7  0
( x – 5)(x – 1) > 0 ( x – 7)(x + 1)  0
x < 1, or x > x > –1, or x  7
Find where these solutions intersect with a number line.
–2 –
x – 4
x – 2
a) integer values for x are 6 and 7
b) the exact area is 8m² if x = 6 and 15m² if x = 7.