Question

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1. Write in interval notation: 2|3-4x|+5>4
2. Write in set builder notation: |2-3x|=|x-3|

Answer 1

Answer:

See bolded below

Step-by-step explanation:

1. First solve the inequality:

2|3-4x|+5>4 [subtract 5 from both sides]

2|3-4x| > - 1 [divide both sides by 2]

|3-4x| > - 1/2

Since all absolute values are always greater than or equal to 0, the solution would be: All Solutions. Respectively in interval notation we have (- ∞, ∞)

2. Start by solving the equation:

|2-3x|=|x-3|,

2-3x = x-3, 2-3x = -(x - 3)

x = 1.25, x = -0.5

In set builder notation: { x | x ∈ {1.25, -0.5} }