Question

Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that have the following solution sets:
two solutions: x=1/2, x=-1/3
one solution: x=-3
all numbers such that x≤5
all numbers that x ≥-1.3

anything helps!

Answer 1

All cases rewritten in the form of difference expressions are listed below:

1. x - 1/2 = 0, x + 1/3 = 0
2. x + 3 = 0
3. x - 5 ≤ 0
4. x + 1/3 ≥ 0

How to translate equalities and inequalities into difference expressions

Equalities represent relationships between two expressions, in which one expression is equal to another. An equality (x = a) is equivalent to the following difference expression:  

x - a = 0   (1)

And inequalities represent relationships between two expressions, in which one expression is not necessarily to another. An inequality (x < a, x > a, x ≤ a, x ≥ a) is represented by the following difference expression:

x - a = b   (2)

Where b have the following cases:

1. If x < a, then b < 0.
2. If x > a, then b > 0.
3. If x ≤ a, then b ≤ 0.
4. If x ≥ a, then b ≥ 0.

Now we proceed to rewrite each case in term of difference expressions:

1. x - 1/2 = 0, x + 1/3 = 0
2. x + 3 = 0
3. x - 5 ≤ 0
4. x + 1/3 ≥ 0

To learn more on inequalities, we kindly invite to check this verified question: brainly.com/question/19491153