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Inequality - College Algebra

by Crystal Elbrecht
(Cincinnati, Ohio)










































can you solve 5x-49> 6-8(2x+7) and write your solution using set builder notation.Please show all of your work

Comments for Inequality - College Algebra

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Mar 20, 2012
Solve 5x - 49 > 6 - 8(2x + 7)
by: Staff


Question:

by Crystal Elbrecht
(Cincinnati, Ohio)

can you solve 5x-49> 6-8(2x+7) and write your solution using set builder notation. Please show all of your work


Answer:

5x - 49 > 6 - 8(2x + 7)

Step 1: Solve for x
Step 2: Write the solution using set builder notation.


I. Solve for x


Use the distributive law to eliminate the parentheses on the right side of the equation

5x - 49 > 6 - 8(2x + 7)

5x - 49 > 6 + (- 8)(2x + 7)

5x - 49 > 6 + (- 8)*(2x) + (- 8)*(7)

5x - 49 > 6 - 16x - 56


Combine like terms on the right side of the equation

5x - 49 > 6 - 16x – 56

5x - 49 > 6 - 56 - 16x

5x - 49 > (6 - 56) - 16x

5x - 49 > - 50 - 16x

5x - 49 > - 16x - 50


Add “16x” to each side of the equation. This will move all the terms containing the “x” variable to the left side of the equation

5x – 49 + 16x > - 16x - 50 + 16x

5x + 16x - 49 > - 16x + 16x - 50

5x + 16x - 49 > (- 16x + 16x) - 50

5x + 16x - 49 > 0 - 50

5x + 16x - 49 > - 50

(5x + 16x) - 49 > - 50

21x - 49 > - 50


Add “49” to each side of the equation. This will remove the 49 from the left side of the equation.

21x - 49 > - 50

21x - 49 + 49 > - 50 + 49

21x + (- 49 + 49) > - 50 + 49

21x + 0 > - 50 + 49

21x > - 50 + 49

21x > (- 50 + 49)

21x > -1


Divide each side of the equation by “21”. This will remove the 21 from the left side of the equation

21x > -1

21x / 21 > -1 / 21

x * (21 / 21) > -1 / 21

x * (1) > -1 / 21

x > -1 / 21


>>> the solution is: x > -1 / 21



2. Write the solution using set builder notation.


There is more than one format for writing the solution in Set Builder Notation.


Here is a commonly used format:


Solution Set = {x | x ∈ ℝ, x > -1 / 21}


{} curly brackets surround the expression
∈ = element of a set
| and : can be used interchangeably. Both notations are separators which mean “where” or “such that”

x: the first “x” is the “output function”, shown as = {x |
x: the second “x” is the “variable”, shown as | x ∈ ℝ,
ℝ (the set of all real numbers) is the” input set”
x > -1 / 21 is the “predicate”


Reading from left to right:

the set of all “x’s” {x | … , …} where “x” is an element of the set of real numbers ℝ { … | x ∈ ℝ, … } and “x” is greater than -1 / 21 {… | … , x > -1 / 21}.



>>> the final answer is: Solution Set = {x | x ∈ ℝ, x > -1 / 21}




Thanks for writing.

Staff
www.solving-math-problems.com



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