# 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

 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